Solve for all values of x by factoring. x^(2)-10 x-6=-2x-6 Answer: x=

Rewrite Equation and Set Equal: Rewrite the equation to bring all terms to one side and set the equation equal to zero. x^2 - 10x - 6 = -2x - 6 Add 2x to both sides to get: x^2 - 10x + 2x - 6 + 6 = 0 Combine like terms: x^2 - 8x = 0Factor Quadratic Equation: Factor the quadratic equation. We can factor out an x from both terms: x(x - 8) = 0Use Zero-Product Property: Use the zero-product property to find the values of x. If a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x: x = 0 or x - 8 = 0 Solving the second equation for x gives us: x = 8

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

\newline

x^{2}-10 x-6=-2 x-6

\newline

Answer:

x=

Rewrite Equation and Set Equal: Rewrite the equation to bring all terms to one side and set the equation equal to zero. $\newline$ $x^2 - 10x - 6 = -2x - 6$ $\newline$ Add $2x$ to both sides to get: $\newline$ $x^2 - 10x + 2x - 6 + 6 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 - 8x = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We can factor out an $x$ from both terms: $\newline$ $x(x - 8) = 0$
Use Zero-Product Property: Use the zero-product property to find the values of $x$ . If a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$ : $x = 0$ or $x - 8 = 0$ Solving the second equation for $x$ gives us: $x = 8$