Solve for all values of x by factoring. x^(2)-4x-60=-3x-4 Answer: x=

Rewrite Equation: Rewrite the equation to bring all terms to one side and set it equal to zero. x^2 - 4x - 60 = -3x - 4 Add 3x and add 4 to both sides to get: x^2 - 4x + 3x - 60 + 4 = 0 Combine like terms: x^2 - x - 56 = 0Factor Quadratic: Factor the quadratic equation. We need to find two numbers that multiply to -56 and add up to -1. The numbers -8 and 7 satisfy these conditions because: -8 * 7 = -56 -8 + 7 = -1 So we can factor the quadratic as: (x - 8)(x + 7) = 0Solve for x: Solve for x by setting each factor equal to zero. First factor: x - 8 = 0 Add 8 to both sides: x = 8 Second factor: x + 7 = 0 Subtract 7 from both sides: x = -7

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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}-4 x-60=-3 x-4

\newline

Answer:

x=

Rewrite Equation: Rewrite the equation to bring all terms to one side and set it equal to zero. $\newline$ $x^2 - 4x - 60 = -3x - 4$ $\newline$ Add $3x$ and add $4$ to both sides to get: $\newline$ $x^2 - 4x + 3x - 60 + 4 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 - x - 56 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-56$ and add up to $-1$ . $\newline$ The numbers $-8$ and $7$ satisfy these conditions because: $\newline$ $-8 \times 7 = -56$ $\newline$ $-8 + 7 = -1$ $\newline$ So we can factor the quadratic as: $\newline$ $(x - 8)(x + 7) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ First factor: $\newline$ $x - 8 = 0$ $\newline$ Add $8$ to both sides: $\newline$ $x = 8$ $\newline$ Second factor: $\newline$ $x + 7 = 0$ $\newline$ Subtract $7$ from both sides: $\newline$ $x = -7$