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$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-30"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?

","comment":{"@type":"Comment","text":"

Choice D is correct. A quadratic equation in the form $ax^{2}+bx+c=0$, where a, b, and c are constants, can be

\\[x=\\frac{-b\\pm\\sqrt{b^{2}-4\\,ac}}{2a}\\]

Subtracting $2x+3$ from both sides of the given equation yields $2x^{2}-2x-5=0$. Applying the quadratic formula, where $a=2,b=-2$, and $c=-5$, yields

\\[x=\\frac{-(-2)\\pm\\sqrt{(-2)^{2}-4(2)(-5)}}{2(2)}\\]

This can be rewritten as $x=\\frac{2\\pm\\sqrt{44}}{4}\\,.$ Since $\\sqrt{44}=\\sqrt{2^{2}(11)}$, or $2\\sqrt{11}$, the equation can be rewritten as $x=\\frac{2\\pm 2\\sqrt{11}}{4}\\,.$ Dividing 2 from both the numerator and denominator yields $\\frac{1+\\sqrt{11}}{2}$ or $\\frac{1-\\sqrt{11}}{2}\\,.$ Of these two solutions, only $\\frac{1+\\sqrt{11}}{2}\\,$ is present among the choices. Thus, the correct choice is D.

Choice A is incorrect and may result from a computational or conceptual error. Choice B is incorrect and may result from using $x=\\frac{-b\\pm\\sqrt{b^{2}-4\\,ac}}{a}\\,$ instead of $x=\\frac{-b\\pm\\sqrt{b^{2}-4\\,ac}}{2a}\\,$ as the quadratic formula. Choice C is incorrect and may result from rewriting $\\sqrt{44}$ as $4\\sqrt{11}$ instead of $2\\sqrt{11}$

"},"encodingFormat":"text/markdown","text":"

$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$2$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$1 -\\sqrt{11}$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$\\dfrac{1}{2}+\\sqrt{11}$

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$\\dfrac{1+\\sqrt{11}}{2}$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-30"}

$2x^{2}-2=2x+3$Which of the following is a solution to the equation above?

$2x^{2}-2=2x+3$Which of the following is a solution to the equation above?

$2x^{2}-2=2x+3$Which of the following is a solution to the equation above?

$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?

$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?

$2x^{2}-2=2x+3$

Which of the following is a solution to the equation above?