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Simplifying (x + 4)(13 + -1x) = (2x + 1) * 2x Reorder the terms: (4 + x)(13 + -1x) = (2x + 1) * 2x Multiply (4 + x) * (13 + -1x) (4(13 + -1x) + x(13 + -1x)) = (2x + 1) * 2x ((13 * 4 + -1x * 4) + x(13 + -1x)) = (2x + 1) * 2x ((52 + -4x) + x(13 + -1x)) = (2x + 1) * 2x (52 + -4x + (13 * x + -1x * x)) = (2x + 1) * 2x (52 + -4x + (13x + -1x2)) = (2x + 1) * 2x Combine like terms: -4x + 13x = 9x (52 + 9x + -1x2) = (2x + 1) * 2x Reorder the terms: 52 + 9x + -1x2 = (1 + 2x) * 2x Reorder the terms for easier multiplication: 52 + 9x + -1x2 = 2x(1 + 2x) 52 + 9x + -1x2 = (1 * 2x + 2x * 2x) 52 + 9x + -1x2 = (2x + 4x2) Solving 52 + 9x + -1x2 = 2x + 4x2 Solving for variable 'x'. Reorder the terms: 52 + 9x + -2x + -1x2 + -4x2 = 2x + 4x2 + -2x + -4x2 Combine like terms: 9x + -2x = 7x 52 + 7x + -1x2 + -4x2 = 2x + 4x2 + -2x + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 52 + 7x + -5x2 = 2x + 4x2 + -2x + -4x2 Reorder the terms: 52 + 7x + -5x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 52 + 7x + -5x2 = 0 + 4x2 + -4x2 52 + 7x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 52 + 7x + -5x2 = 0 Factor a trinomial. (4 + -1x)(13 + 5x) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(13 + 5x)' equal to zero and attempt to solve: Simplifying 13 + 5x = 0 Solving 13 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 5x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5x = 0 + -13 5x = 0 + -13 Combine like terms: 0 + -13 = -13 5x = -13 Divide each side by '5'. x = -2.6 Simplifying x = -2.6Solution
x = {4, -2.6}
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