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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

If $3 x^{2} - 18 x - 15 = 0$ , what is the value of $x^{2} - 6 x$ ?

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ExplanationShow

The correct answer is $5$ . Dividing each side of the given equation by $3$ yields $x^{2} - 6 x - 5 = 0$ . Adding $5$ to each side of this equation yields $x^{2} - 6 x = 5$ . Therefore, if $3 x^{2} - 18 x - 15 = 0$ , the value of $x^{2} - 6 x$ is $5$ .

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