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Simplifying 2x2 + 18x + 37 = (x + 4)(x + 4) Reorder the terms: 37 + 18x + 2x2 = (x + 4)(x + 4) Reorder the terms: 37 + 18x + 2x2 = (4 + x)(x + 4) Reorder the terms: 37 + 18x + 2x2 = (4 + x)(4 + x) Multiply (4 + x) * (4 + x) 37 + 18x + 2x2 = (4(4 + x) + x(4 + x)) 37 + 18x + 2x2 = ((4 * 4 + x * 4) + x(4 + x)) 37 + 18x + 2x2 = ((16 + 4x) + x(4 + x)) 37 + 18x + 2x2 = (16 + 4x + (4 * x + x * x)) 37 + 18x + 2x2 = (16 + 4x + (4x + x2)) Combine like terms: 4x + 4x = 8x 37 + 18x + 2x2 = (16 + 8x + x2) Solving 37 + 18x + 2x2 = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: 37 + -16 + 18x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 37 + -16 = 21 21 + 18x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 18x + -8x = 10x 21 + 10x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 21 + 10x + 1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: 21 + 10x + 1x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 21 + 10x + 1x2 = 0 + 8x + -8x + x2 + -1x2 21 + 10x + 1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 21 + 10x + 1x2 = 0 + x2 + -1x2 21 + 10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 10x + 1x2 = 0 Factor a trinomial. (7 + x)(3 + x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-7, -3}
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