Solve the quadratic by factoring. 2x^(2)+9x+12=8 Answer: x=

Subtract 8: Subtract 8 from both sides of the equation to set it equal to zero. 2x^2 + 9x + 12 - 8 = 0 2x^2 + 9x + 4 = 0Identify a, b, c: Identify a, b, and c in the quadratic equation 2x^2 + 9x + 4. a = 2, b = 9, c = 4Find two numbers: Find two numbers that multiply to a*c (2*4 = 8) and add up to b (9). The numbers are 1 and 8 because 1*8 = 8 and 1+8 = 9.Rewrite middle term: Rewrite the middle term (9x) using the two numbers found in Step 3. 2x^2 + 1x + 8x + 4 = 0Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2x^2 + 1x) + (8x + 4) = 0 Factor out the greatest common factor from each group. x(2x + 1) + 4(2x + 1) = 0Factor out common binomial: Factor out the common binomial factor. (2x + 1)(x + 4) = 0Set factors equal: Set each factor equal to zero and solve for x. 2x + 1 = 0 or x + 4 = 0 x = -1/2 or x = -4

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Solve the quadratic by factoring.

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2 x^{2}+9 x+12=8

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Answer:

x=

Subtract $8$ : Subtract $8$ from both sides of the equation to set it equal to zero. $\newline$ $2x^2 + 9x + 12 - 8 = 0$ $\newline$ $2x^2 + 9x + 4 = 0$
Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic equation $2x^2 + 9x + 4$ . $\newline$ $a = 2$ , $b = 9$ , $c = 4$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*4 = 8$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers are $1$ and $8$ because $1*8 = 8$ and $1+8 = 9$ .
Rewrite middle term: Rewrite the middle term $9x$ using the two numbers found in Step $3$ . $2x^2 + 1x + 8x + 4 = 0$
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms. $\newline$ $(2x^2 + 1x) + (8x + 4) = 0$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $x(2x + 1) + 4(2x + 1) = 0$
Factor out common binomial: Factor out the common binomial factor. $\newline$ $(2x + 1)(x + 4) = 0$
Set factors equal: Set each factor equal to zero and solve for $x$ . $2x + 1 = 0$ or $x + 4 = 0$ $x = -\frac{1}{2}$ or $x = -4$