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Simplifying 5(2x + 1) * 7(4x + 2) = 0 Reorder the terms: 5(1 + 2x) * 7(4x + 2) = 0 Reorder the terms: 5(1 + 2x) * 7(2 + 4x) = 0 Reorder the terms for easier multiplication: 5 * 7(1 + 2x)(2 + 4x) = 0 Multiply 5 * 7 35(1 + 2x)(2 + 4x) = 0 Multiply (1 + 2x) * (2 + 4x) 35(1(2 + 4x) + 2x * (2 + 4x)) = 0 35((2 * 1 + 4x * 1) + 2x * (2 + 4x)) = 0 35((2 + 4x) + 2x * (2 + 4x)) = 0 35(2 + 4x + (2 * 2x + 4x * 2x)) = 0 35(2 + 4x + (4x + 8x2)) = 0 Combine like terms: 4x + 4x = 8x 35(2 + 8x + 8x2) = 0 (2 * 35 + 8x * 35 + 8x2 * 35) = 0 (70 + 280x + 280x2) = 0 Solving 70 + 280x + 280x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '70'. 70(1 + 4x + 4x2) = 0 Factor a trinomial. 70((1 + 2x)(1 + 2x)) = 0 Ignore the factor 70.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.5, -0.5}
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