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Simplifying (2x + -7)(2x + 7) + (x + -3)(x + 3) = 4x2 + 8x + -73 Reorder the terms: (-7 + 2x)(2x + 7) + (x + -3)(x + 3) = 4x2 + 8x + -73 Reorder the terms: (-7 + 2x)(7 + 2x) + (x + -3)(x + 3) = 4x2 + 8x + -73 Multiply (-7 + 2x) * (7 + 2x) (-7(7 + 2x) + 2x * (7 + 2x)) + (x + -3)(x + 3) = 4x2 + 8x + -73 ((7 * -7 + 2x * -7) + 2x * (7 + 2x)) + (x + -3)(x + 3) = 4x2 + 8x + -73 ((-49 + -14x) + 2x * (7 + 2x)) + (x + -3)(x + 3) = 4x2 + 8x + -73 (-49 + -14x + (7 * 2x + 2x * 2x)) + (x + -3)(x + 3) = 4x2 + 8x + -73 (-49 + -14x + (14x + 4x2)) + (x + -3)(x + 3) = 4x2 + 8x + -73 Combine like terms: -14x + 14x = 0 (-49 + 0 + 4x2) + (x + -3)(x + 3) = 4x2 + 8x + -73 (-49 + 4x2) + (x + -3)(x + 3) = 4x2 + 8x + -73 Reorder the terms: -49 + 4x2 + (-3 + x)(x + 3) = 4x2 + 8x + -73 Reorder the terms: -49 + 4x2 + (-3 + x)(3 + x) = 4x2 + 8x + -73 Multiply (-3 + x) * (3 + x) -49 + 4x2 + (-3(3 + x) + x(3 + x)) = 4x2 + 8x + -73 -49 + 4x2 + ((3 * -3 + x * -3) + x(3 + x)) = 4x2 + 8x + -73 -49 + 4x2 + ((-9 + -3x) + x(3 + x)) = 4x2 + 8x + -73 -49 + 4x2 + (-9 + -3x + (3 * x + x * x)) = 4x2 + 8x + -73 -49 + 4x2 + (-9 + -3x + (3x + x2)) = 4x2 + 8x + -73 Combine like terms: -3x + 3x = 0 -49 + 4x2 + (-9 + 0 + x2) = 4x2 + 8x + -73 -49 + 4x2 + (-9 + x2) = 4x2 + 8x + -73 Reorder the terms: -49 + -9 + 4x2 + x2 = 4x2 + 8x + -73 Combine like terms: -49 + -9 = -58 -58 + 4x2 + x2 = 4x2 + 8x + -73 Combine like terms: 4x2 + x2 = 5x2 -58 + 5x2 = 4x2 + 8x + -73 Reorder the terms: -58 + 5x2 = -73 + 8x + 4x2 Solving -58 + 5x2 = -73 + 8x + 4x2 Solving for variable 'x'. Reorder the terms: -58 + 73 + -8x + 5x2 + -4x2 = -73 + 8x + 4x2 + 73 + -8x + -4x2 Combine like terms: -58 + 73 = 15 15 + -8x + 5x2 + -4x2 = -73 + 8x + 4x2 + 73 + -8x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 15 + -8x + 1x2 = -73 + 8x + 4x2 + 73 + -8x + -4x2 Reorder the terms: 15 + -8x + 1x2 = -73 + 73 + 8x + -8x + 4x2 + -4x2 Combine like terms: -73 + 73 = 0 15 + -8x + 1x2 = 0 + 8x + -8x + 4x2 + -4x2 15 + -8x + 1x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 15 + -8x + 1x2 = 0 + 4x2 + -4x2 15 + -8x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 15 + -8x + 1x2 = 0 Factor a trinomial. (3 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = {3, 5}
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