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Simplifying 8(x + 0.75)(x + 0.5) = 0 Reorder the terms: 8(0.75 + x)(x + 0.5) = 0 Reorder the terms: 8(0.75 + x)(0.5 + x) = 0 Multiply (0.75 + x) * (0.5 + x) 8(0.75(0.5 + x) + x(0.5 + x)) = 0 8((0.5 * 0.75 + x * 0.75) + x(0.5 + x)) = 0 8((0.375 + 0.75x) + x(0.5 + x)) = 0 8(0.375 + 0.75x + (0.5 * x + x * x)) = 0 8(0.375 + 0.75x + (0.5x + x2)) = 0 Combine like terms: 0.75x + 0.5x = 1.25x 8(0.375 + 1.25x + x2) = 0 (0.375 * 8 + 1.25x * 8 + x2 * 8) = 0 (3 + 10x + 8x2) = 0 Solving 3 + 10x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 4x)(1 + 2x) = 0Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Subproblem 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 = {-0.75, -0.5}
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