Solve the quadratic by factoring. x^(2)+4x+32=-8x-3 Answer: x=

Write Equation and Rearrange: Write down the given equation and move all terms to one side to set the equation to zero. x^2 + 4x + 32 = -8x - 3 Add 8x to both sides and add 3 to both sides to get: x^2 + 12x + 35 = 0Identify Coefficients: Identify a, b, and c in the quadratic equation ax^2 + bx + c = 0. Here, a = 1, b = 12, and c = 35.Find Multiplying Numbers: Find two numbers that multiply to ac (which is 35) and add up to b (which is 12). The numbers 5 and 7 multiply to 35 and add up to 12. 5 * 7 = 35 5 + 7 = 12Split Middle Term: Write the quadratic equation with the middle term split using the two numbers found in Step 3. x^2 + 5x + 7x + 35 = 0Factor by Grouping: Factor by grouping. Group the terms to factor out the common factors: x(x + 5) + 7(x + 5) = 0Factor out Common Factor: Factor out the common binomial factor. (x + 5)(x + 7) = 0Set Factors Equal and Solve: Set each factor equal to zero and solve for x. x + 5 = 0 or x + 7 = 0 x = -5 or x = -7

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Solve the quadratic by factoring.

x^(2)+4x+32=-8x-3
Answer:
x=

Solve the quadratic by factoring. $\newline$ $x^{2}+4 x+32=-8 x-3$ $\newline$ Answer: $x=$

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

\newline

x^{2}+4 x+32=-8 x-3

\newline

Answer:

x=

Write Equation and Rearrange: Write down the given equation and move all terms to one side to set the equation to zero. $\newline$ $x^2 + 4x + 32 = -8x - 3$ $\newline$ Add $8x$ to both sides and add $3$ to both sides to get: $\newline$ $x^2 + 12x + 35 = 0$
Identify Coefficients: Identify $a$ , $b$ , and $c$ in the quadratic equation $ax^2 + bx + c = 0$ . Here, $a = 1$ , $b = 12$ , and $c = 35$ .
Find Multiplying Numbers: Find two numbers that multiply to $ac$ (which is $35$ ) and add up to $b$ (which is $12$ ). $\newline$ The numbers $5$ and $7$ multiply to $35$ and add up to $12$ . $\newline$ $5 \times 7 = 35$ $\newline$ $5 + 7 = 12$
Split Middle Term: Write the quadratic equation with the middle term split using the two numbers found in Step $3$ . $x^2 + 5x + 7x + 35 = 0$
Factor by Grouping: Factor by grouping. $\newline$ Group the terms to factor out the common factors: $\newline$ $x(x + 5) + 7(x + 5) = 0$
Factor out Common Factor: Factor out the common binomial factor. x + \(5)(x + $7$ ) = $0$ \
Set Factors Equal and Solve: Set each factor equal to zero and solve for $x$ . $x + 5 = 0$ or $x + 7 = 0$ $x = -5$ or $x = -7$