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Simplifying 456 = (20 + 2x)(15 + 2x) Multiply (20 + 2x) * (15 + 2x) 456 = (20(15 + 2x) + 2x * (15 + 2x)) 456 = ((15 * 20 + 2x * 20) + 2x * (15 + 2x)) 456 = ((300 + 40x) + 2x * (15 + 2x)) 456 = (300 + 40x + (15 * 2x + 2x * 2x)) 456 = (300 + 40x + (30x + 4x2)) Combine like terms: 40x + 30x = 70x 456 = (300 + 70x + 4x2) Solving 456 = 300 + 70x + 4x2 Solving for variable 'x'. Combine like terms: 456 + -300 = 156 156 + -70x + -4x2 = 300 + 70x + 4x2 + -300 + -70x + -4x2 Reorder the terms: 156 + -70x + -4x2 = 300 + -300 + 70x + -70x + 4x2 + -4x2 Combine like terms: 300 + -300 = 0 156 + -70x + -4x2 = 0 + 70x + -70x + 4x2 + -4x2 156 + -70x + -4x2 = 70x + -70x + 4x2 + -4x2 Combine like terms: 70x + -70x = 0 156 + -70x + -4x2 = 0 + 4x2 + -4x2 156 + -70x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 156 + -70x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(78 + -35x + -2x2) = 0 Factor a trinomial. 2((2 + -1x)(39 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(39 + 2x)' equal to zero and attempt to solve: Simplifying 39 + 2x = 0 Solving 39 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 2x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 2x = 0 + -39 2x = 0 + -39 Combine like terms: 0 + -39 = -39 2x = -39 Divide each side by '2'. x = -19.5 Simplifying x = -19.5Solution
x = {2, -19.5}
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