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Simplifying 180 = 18x(16x + 4) Reorder the terms: 180 = 18x(4 + 16x) 180 = (4 * 18x + 16x * 18x) 180 = (72x + 288x2) Solving 180 = 72x + 288x2 Solving for variable 'x'. Reorder the terms: 180 + -72x + -288x2 = 72x + -72x + 288x2 + -288x2 Combine like terms: 72x + -72x = 0 180 + -72x + -288x2 = 0 + 288x2 + -288x2 180 + -72x + -288x2 = 288x2 + -288x2 Combine like terms: 288x2 + -288x2 = 0 180 + -72x + -288x2 = 0 Factor out the Greatest Common Factor (GCF), '36'. 36(5 + -2x + -8x2) = 0 Ignore the factor 36.Subproblem 1
Set the factor '(5 + -2x + -8x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + -8x2 = 0 Solving 5 + -2x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.25x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.25x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.25x + x2 = 0 + 0.625 0.25x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.25x + x2 = 0.625 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.625 + 0.015625 Combine like terms: 0.625 + 0.015625 = 0.640625 0.015625 + 0.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 0.125) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 0.125 = 0.80039053 Simplifying x + 0.125 = 0.80039053 Reorder the terms: 0.125 + x = 0.80039053 Solving 0.125 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.80039053 + -0.125 x = 0.80039053 + -0.125 Combine like terms: 0.80039053 + -0.125 = 0.67539053 x = 0.67539053 Simplifying x = 0.67539053Subproblem 2
x + 0.125 = -0.80039053 Simplifying x + 0.125 = -0.80039053 Reorder the terms: 0.125 + x = -0.80039053 Solving 0.125 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.80039053 + -0.125 x = -0.80039053 + -0.125 Combine like terms: -0.80039053 + -0.125 = -0.92539053 x = -0.92539053 Simplifying x = -0.92539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67539053, -0.92539053}Solution
x = {0.67539053, -0.92539053}
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