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Simplifying ((5 + 2x)(4 + 2x) + -20) = 0 Multiply (5 + 2x) * (4 + 2x) ((5(4 + 2x) + 2x * (4 + 2x)) + -20) = 0 (((4 * 5 + 2x * 5) + 2x * (4 + 2x)) + -20) = 0 (((20 + 10x) + 2x * (4 + 2x)) + -20) = 0 ((20 + 10x + (4 * 2x + 2x * 2x)) + -20) = 0 ((20 + 10x + (8x + 4x2)) + -20) = 0 Combine like terms: 10x + 8x = 18x ((20 + 18x + 4x2) + -20) = 0 Reorder the terms: (20 + -20 + 18x + 4x2) = 0 Combine like terms: 20 + -20 = 0 (0 + 18x + 4x2) = 0 (18x + 4x2) = 0 Remove parenthesis around (18x + 4x2) 18x + 4x2 = 0 Solving 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Solution
x = {0, -4.5}
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