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Simplifying 5(x + 2)(x + 2) + -29(x + 2) = 6 Reorder the terms: 5(2 + x)(x + 2) + -29(x + 2) = 6 Reorder the terms: 5(2 + x)(2 + x) + -29(x + 2) = 6 Multiply (2 + x) * (2 + x) 5(2(2 + x) + x(2 + x)) + -29(x + 2) = 6 5((2 * 2 + x * 2) + x(2 + x)) + -29(x + 2) = 6 5((4 + 2x) + x(2 + x)) + -29(x + 2) = 6 5(4 + 2x + (2 * x + x * x)) + -29(x + 2) = 6 5(4 + 2x + (2x + x2)) + -29(x + 2) = 6 Combine like terms: 2x + 2x = 4x 5(4 + 4x + x2) + -29(x + 2) = 6 (4 * 5 + 4x * 5 + x2 * 5) + -29(x + 2) = 6 (20 + 20x + 5x2) + -29(x + 2) = 6 Reorder the terms: 20 + 20x + 5x2 + -29(2 + x) = 6 20 + 20x + 5x2 + (2 * -29 + x * -29) = 6 20 + 20x + 5x2 + (-58 + -29x) = 6 Reorder the terms: 20 + -58 + 20x + -29x + 5x2 = 6 Combine like terms: 20 + -58 = -38 -38 + 20x + -29x + 5x2 = 6 Combine like terms: 20x + -29x = -9x -38 + -9x + 5x2 = 6 Solving -38 + -9x + 5x2 = 6 Solving for variable 'x'. Reorder the terms: -38 + -6 + -9x + 5x2 = 6 + -6 Combine like terms: -38 + -6 = -44 -44 + -9x + 5x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -44 + -9x + 5x2 = 0 Factor a trinomial. (-11 + -5x)(4 + -1x) = 0Subproblem 1
Set the factor '(-11 + -5x)' equal to zero and attempt to solve: Simplifying -11 + -5x = 0 Solving -11 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5x = 0 + 11 -5x = 0 + 11 Combine like terms: 0 + 11 = 11 -5x = 11 Divide each side by '-5'. x = -2.2 Simplifying x = -2.2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2.2, 4}
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