Solve the quadratic by factoring. 2x^(2)-19 x-8=-4x Answer: x=

Move Terms to One Side: Move all terms to one side of the equation to set the equation to zero. 2x^2 - 19x - 8 = -4x Add 4x to both sides to get: 2x^2 - 19x + 4x - 8 = 0 Combine like terms: 2x^2 - 15x - 8 = 0Add 4x to Both Sides: Factor the quadratic equation 2x^2 - 15x - 8. We need to find two numbers that multiply to 2 * -8 = -16 and add up to -15. The numbers -16 and 1 have a product of -16 and a sum of -15. Rewrite the middle term using -16x and 1x: 2x^2 - 16x + 1x - 8 = 0Factor Quadratic Equation: Group the terms to factor by grouping. (2x^2 - 16x) + (1x - 8) = 0 Factor out the greatest common factor from each group: 2x(x - 8) + 1(x - 8) = 0Rewrite Middle Term: Factor out the common binomial factor (x - 8). (2x + 1)(x - 8) = 0Group Terms for Factoring: Set each factor equal to zero and solve for x. 2x + 1 = 0 or x - 8 = 0 For 2x + 1 = 0: 2x = -1 x = -1/2 For x - 8 = 0: x = 8

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Solve the quadratic by factoring.

\newline

2 x^{2}-19 x-8=-4 x

\newline

Answer:

x=

Move Terms to One Side: Move all terms to one side of the equation to set the equation to zero. $\newline$ $2x^2 - 19x - 8 = -4x$ $\newline$ Add $4x$ to both sides to get: $\newline$ $2x^2 - 19x + 4x - 8 = 0$ $\newline$ Combine like terms: $\newline$ $2x^2 - 15x - 8 = 0$
Add $4x$ to Both Sides: Factor the quadratic equation $2x^2 - 15x - 8$ . We need to find two numbers that multiply to $2 \times -8 = -16$ and add up to $-15$ . The numbers $-16$ and $1$ have a product of $-16$ and a sum of $-15$ . Rewrite the middle term using $-16x$ and $1x$ : $2x^2 - 15x - 8$ $0$
Factor Quadratic Equation: Group the terms to factor by grouping. $\newline$ $(2x^2 - 16x) + (1x - 8) = 0$ $\newline$ Factor out the greatest common factor from each group: $\newline$ $2x(x - 8) + 1(x - 8) = 0$
Rewrite Middle Term: Factor out the common binomial factor $(x - 8)$ . $\newline$ $(2x + 1)(x - 8) = 0$
Group Terms for Factoring: Set each factor equal to zero and solve for $x$ . $2x + 1 = 0$ or $x - 8 = 0$ For $2x + 1 = 0$ : $2x = -1$ $x = -\frac{1}{2}$ For $x - 8 = 0$ : $x = 8$