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Simplifying -16x2 + -36x + -10 = 0 Reorder the terms: -10 + -36x + -16x2 = 0 Solving -10 + -36x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 18x + 8x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 18x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + 18x + 8x2 = 0 Solving 5 + 18x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 2.25x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 2.25x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 2.25x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 2.25x + x2 = 0 + -0.625 2.25x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 2.25x + x2 = -0.625 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -0.625 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -0.625 + 1.265625 Combine like terms: -0.625 + 1.265625 = 0.640625 1.265625 + 2.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 1.125) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 1.125 = 0.80039053 Simplifying x + 1.125 = 0.80039053 Reorder the terms: 1.125 + x = 0.80039053 Solving 1.125 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.80039053 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.80039053 + -1.125 x = 0.80039053 + -1.125 Combine like terms: 0.80039053 + -1.125 = -0.32460947 x = -0.32460947 Simplifying x = -0.32460947Subproblem 2
x + 1.125 = -0.80039053 Simplifying x + 1.125 = -0.80039053 Reorder the terms: 1.125 + x = -0.80039053 Solving 1.125 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.80039053 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.80039053 + -1.125 x = -0.80039053 + -1.125 Combine like terms: -0.80039053 + -1.125 = -1.92539053 x = -1.92539053 Simplifying x = -1.92539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.32460947, -1.92539053}Solution
x = {-0.32460947, -1.92539053}
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