// Numbas version: finer_feedback_settings
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"disc", "group": "Ungrouped variables", "definition": "(lcoeff^2-4*scoeff*ccoeff)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "dd", "d", "scoeff", "lcoeff", "ccoeff", "disc", "lengthdet", "div", "argtop", "argbot", "sqrtargtop", "sqrtargbot"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Fill in the blanks to solve the quadratic by&nbsp;completing the square:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td>$\\simplify{{scoeff}x^2+{lcoeff}x+{ccoeff+c}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{c}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$\\simplify{{scoeff}x^2+{lcoeff}x}$&nbsp;</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$x^2+$[[1]]$x$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">[[2]]</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$x^2+$[[1]]$x+$[[3]]</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">[[4]]</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$(x+$[[5]]$)^2$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">[[4]]</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$(x+$[[5]]$)$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\pm$[[6]]</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Longrightarrow$</td>\n<td style=\"text-align: right;\">$x$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">[[7]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><strong>Note:</strong> In the last&nbsp;gap, if $x=1,2$, enter <strong>set(1,2)</strong>.</p>", "stepsPenalty": "8", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Recall&nbsp;</p>\n<p style=\"text-align: center;\">$(x+a)^2=x^2+2ax+a^2$</p>\n<p>is called a perfect square. Now, notice if we let $b=2a$ this equation would become</p>\n<p style=\"text-align: center;\">$\\left(x+\\frac{b}{2}\\right)^2=x^2+bx+\\left(\\frac{b}{2}\\right)^2$.</p>\n<p></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>$\\simplify{{scoeff}x^2+{lcoeff}x+{ccoeff+c}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{c}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify{{scoeff}x^2+{lcoeff}x}$&nbsp;</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{-ccoeff}$</td>\n<td style=\"text-align: left;\">(get all constants on the right hand side)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x^2+\\simplify{{lcoeff}/{scoeff}}x$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{-ccoeff}/{scoeff}}$</td>\n<td style=\"text-align: left;\">(divide every term by the coefficient of $x^2$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x^2+\\simplify{{lcoeff}/{scoeff}}x+\\simplify{{lcoeff^2}/{4*scoeff^2}}$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{argtop}/{argbot}}$</td>\n<td style=\"text-align: left;\">(halve the coefficient of $x$, then square, then add to both sides)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$(x+\\simplify{{lcoeff}/{2*scoeff}})^2$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{argtop}/{argbot}}$</td>\n<td style=\"text-align: left;\">(rewrite the left hand side&nbsp;as a perfect square)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$(x+\\simplify{{lcoeff}/{2*scoeff}})$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\pm \\simplify{{sqrtargtop}/{sqrtargbot}}$</td>\n<td style=\"text-align: left;\">(take the plus or minus square root of both sides)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\simplify{{-c}/{a}},\\simplify{{-d}/{b}}$</td>\n<td style=\"text-align: left;\">(solve for $x$)</td>\n</tr>\n</tbody>\n</table>\n<p><strong>Note:</strong> we would enter the final answer as set$\\left(\\simplify{{-c}/{a}},\\simplify{{-d}/{b}}\\right)$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{-ccoeff}", "maxValue": "{-ccoeff}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], 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