{"@context":"https://schema.org/","@type":"Quiz","name":"

$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?

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$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?

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

Choice D is correct. Adding 10 to each side of the given equation yields $x^{2}-40x=10$. To complete the square, adding $\\left(\\frac{40}{2}\\right)^{2}$, or $20^{2}$, to each side of this equation yields $x^{2}-40x+20^{2}=10+20^{2}$, or $\\left(x-20\\right)^{2}=410$. Taking the square root of each side of this equation yields $x-20=\\pm\\sqrt{410}$. Adding 20 to each side of this equation yields $x=20\\pm\\sqrt{410}$. Therefore, the solutions to the given equation are $x=20+\\sqrt{410}$ and $x=20-\\sqrt{410}$. The sum of these solutions is $(20+\\sqrt{410})+(20+\\sqrt{410})$, or $40$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

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

$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?

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

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

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

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

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

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-164"}

$$x^{2}-40x-10=0$$What is the sum of the solutions to the given equation?

$$x^{2}-40x-10=0$$What is the sum of the solutions to the given equation?

$$x^{2}-40x-10=0$$What is the sum of the solutions to the given equation?

$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?

$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?

$$x^{2}-40x-10=0$$

What is the sum of the solutions to the given equation?