Solve for all values of x by factoring. x^(2)-7x-36=-2x Answer: x=

Rewrite Equation: Rewrite the equation to bring all terms to one side. We start by adding 2x to both sides of the equation to get a standard quadratic equation form. x^2 - 7x - 36 = -2x x^2 - 7x + 2x - 36 = 0 x^2 - 5x - 36 = 0Factor Quadratic: Factor the quadratic equation. We need to find two numbers that multiply to -36 and add up to -5. The numbers that satisfy these conditions are -9 and 4 because -9 * 4 = -36 and -9 + 4 = -5. So, we can write the factored form as: (x - 9)(x + 4) = 0Solve for x: Solve for x by setting each factor equal to zero. First factor: x - 9 = 0 x = 9 Second factor: x + 4 = 0 x = -4

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

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x^{2}-7 x-36=-2 x

\newline

Answer:

x=

Rewrite Equation: Rewrite the equation to bring all terms to one side. $\newline$ We start by adding $2x$ to both sides of the equation to get a standard quadratic equation form. $\newline$ $x^2 - 7x - 36 = -2x$ $\newline$ $x^2 - 7x + 2x - 36 = 0$ $\newline$ $x^2 - 5x - 36 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-36$ and add up to $-5$ . The numbers that satisfy these conditions are $-9$ and $4$ because $-9 \times 4 = -36$ and $-9 + 4 = -5$ . $\newline$ So, we can write the factored form as: $\newline$ $(x - 9)(x + 4) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ First factor: $\newline$ $x - 9 = 0$ $\newline$ $x = 9$ $\newline$ Second factor: $\newline$ $x + 4 = 0$ $\newline$ $x = -4$