Solve the quadratic by factoring. x^(2)-12 x=-5x-12 Answer: x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation. x^2 - 12x = -5x - 12 Add 5x and 12 to both sides to get: x^2 - 12x + 5x + 12 = 0 Combine like terms: x^2 - 7x + 12 = 0Factor the Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to 12 (the constant term) and add up to -7 (the coefficient of the x term). The numbers that satisfy these conditions are -3 and -4. -3 * -4 = 12 -3 + -4 = -7 So we can factor the quadratic as: (x - 3)(x - 4) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 3 = 0 or x - 4 = 0 If x - 3 = 0, then x = 3. If x - 4 = 0, then x = 4.

Home

Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

\newline

x^{2}-12 x=-5 x-12

\newline

Answer:

x=

Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation. $\newline$ $x^2 - 12x = -5x - 12$ $\newline$ Add $5x$ and $12$ to both sides to get: $\newline$ $x^2 - 12x + 5x + 12 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 - 7x + 12 = 0$
Factor the Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $12$ (the constant term) and add up to $-7$ (the coefficient of the $x$ term). $\newline$ The numbers that satisfy these conditions are $-3$ and $-4$ . $\newline$ $-3 \times -4 = 12$ $\newline$ $-3 + -4 = -7$ $\newline$ So we can factor the quadratic as: $\newline$ $(x - 3)(x - 4) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 3 = 0$ or $x - 4 = 0$ $\newline$ If $x - 3 = 0$ , then $x = 3$ . $\newline$ If $x - 4 = 0$ , then $x = 4$ .