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Simplifying (3x + 4)(5x + -7) = (2x + 7)(2x + 7) + 53 Reorder the terms: (4 + 3x)(5x + -7) = (2x + 7)(2x + 7) + 53 Reorder the terms: (4 + 3x)(-7 + 5x) = (2x + 7)(2x + 7) + 53 Multiply (4 + 3x) * (-7 + 5x) (4(-7 + 5x) + 3x * (-7 + 5x)) = (2x + 7)(2x + 7) + 53 ((-7 * 4 + 5x * 4) + 3x * (-7 + 5x)) = (2x + 7)(2x + 7) + 53 ((-28 + 20x) + 3x * (-7 + 5x)) = (2x + 7)(2x + 7) + 53 (-28 + 20x + (-7 * 3x + 5x * 3x)) = (2x + 7)(2x + 7) + 53 (-28 + 20x + (-21x + 15x2)) = (2x + 7)(2x + 7) + 53 Combine like terms: 20x + -21x = -1x (-28 + -1x + 15x2) = (2x + 7)(2x + 7) + 53 Reorder the terms: -28 + -1x + 15x2 = (7 + 2x)(2x + 7) + 53 Reorder the terms: -28 + -1x + 15x2 = (7 + 2x)(7 + 2x) + 53 Multiply (7 + 2x) * (7 + 2x) -28 + -1x + 15x2 = (7(7 + 2x) + 2x * (7 + 2x)) + 53 -28 + -1x + 15x2 = ((7 * 7 + 2x * 7) + 2x * (7 + 2x)) + 53 -28 + -1x + 15x2 = ((49 + 14x) + 2x * (7 + 2x)) + 53 -28 + -1x + 15x2 = (49 + 14x + (7 * 2x + 2x * 2x)) + 53 -28 + -1x + 15x2 = (49 + 14x + (14x + 4x2)) + 53 Combine like terms: 14x + 14x = 28x -28 + -1x + 15x2 = (49 + 28x + 4x2) + 53 Reorder the terms: -28 + -1x + 15x2 = 49 + 53 + 28x + 4x2 Combine like terms: 49 + 53 = 102 -28 + -1x + 15x2 = 102 + 28x + 4x2 Solving -28 + -1x + 15x2 = 102 + 28x + 4x2 Solving for variable 'x'. Reorder the terms: -28 + -102 + -1x + -28x + 15x2 + -4x2 = 102 + 28x + 4x2 + -102 + -28x + -4x2 Combine like terms: -28 + -102 = -130 -130 + -1x + -28x + 15x2 + -4x2 = 102 + 28x + 4x2 + -102 + -28x + -4x2 Combine like terms: -1x + -28x = -29x -130 + -29x + 15x2 + -4x2 = 102 + 28x + 4x2 + -102 + -28x + -4x2 Combine like terms: 15x2 + -4x2 = 11x2 -130 + -29x + 11x2 = 102 + 28x + 4x2 + -102 + -28x + -4x2 Reorder the terms: -130 + -29x + 11x2 = 102 + -102 + 28x + -28x + 4x2 + -4x2 Combine like terms: 102 + -102 = 0 -130 + -29x + 11x2 = 0 + 28x + -28x + 4x2 + -4x2 -130 + -29x + 11x2 = 28x + -28x + 4x2 + -4x2 Combine like terms: 28x + -28x = 0 -130 + -29x + 11x2 = 0 + 4x2 + -4x2 -130 + -29x + 11x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -130 + -29x + 11x2 = 0 Factor a trinomial. (-26 + -11x)(5 + -1x) = 0Subproblem 1
Set the factor '(-26 + -11x)' equal to zero and attempt to solve: Simplifying -26 + -11x = 0 Solving -26 + -11x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + -11x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -11x = 0 + 26 -11x = 0 + 26 Combine like terms: 0 + 26 = 26 -11x = 26 Divide each side by '-11'. x = -2.363636364 Simplifying x = -2.363636364Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2.363636364, 5}
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