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Simplifying 32x2 + 12x + -32 = 0 Reorder the terms: -32 + 12x + 32x2 = 0 Solving -32 + 12x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 3x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + 8x2 = 0 Solving -8 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + 0.375x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.375x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.375x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.375x + x2 = 0 + 1 0.375x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.375x + x2 = 1 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 1 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 1 + 0.03515625 Combine like terms: 1 + 0.03515625 = 1.03515625 0.03515625 + 0.375x + x2 = 1.03515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 1.03515625 Calculate the square root of the right side: 1.017426287 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.017426287 and -1.017426287.Subproblem 1
x + 0.1875 = 1.017426287 Simplifying x + 0.1875 = 1.017426287 Reorder the terms: 0.1875 + x = 1.017426287 Solving 0.1875 + x = 1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.017426287 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.017426287 + -0.1875 x = 1.017426287 + -0.1875 Combine like terms: 1.017426287 + -0.1875 = 0.829926287 x = 0.829926287 Simplifying x = 0.829926287Subproblem 2
x + 0.1875 = -1.017426287 Simplifying x + 0.1875 = -1.017426287 Reorder the terms: 0.1875 + x = -1.017426287 Solving 0.1875 + x = -1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.017426287 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.017426287 + -0.1875 x = -1.017426287 + -0.1875 Combine like terms: -1.017426287 + -0.1875 = -1.204926287 x = -1.204926287 Simplifying x = -1.204926287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.829926287, -1.204926287}Solution
x = {0.829926287, -1.204926287}
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