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Simplifying [(x + -5)(x + 3)] + 16 = 0 Reorder the terms: [(-5 + x)(x + 3)] + 16 = 0 Reorder the terms: [(-5 + x)(3 + x)] + 16 = 0 Multiply (-5 + x) * (3 + x) [(-5(3 + x) + x(3 + x))] + 16 = 0 [((3 * -5 + x * -5) + x(3 + x))] + 16 = 0 [((-15 + -5x) + x(3 + x))] + 16 = 0 [(-15 + -5x + (3 * x + x * x))] + 16 = 0 [(-15 + -5x + (3x + x2))] + 16 = 0 Combine like terms: -5x + 3x = -2x [(-15 + -2x + x2)] + 16 = 0 [-15 + -2x + x2] + 16 = 0 Remove brackets around [-15 + -2x + x2] -15 + -2x + x2 + 16 = 0 Reorder the terms: -15 + 16 + -2x + x2 = 0 Combine like terms: -15 + 16 = 1 1 + -2x + x2 = 0 Solving 1 + -2x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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