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Simplifying 8x2 + 8x + -252 = 0 Reorder the terms: -252 + 8x + 8x2 = 0 Solving -252 + 8x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + 2x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-63 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -63 + 2x + 2x2 = 0 Solving -63 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x + x2 = 0 + 31.5 x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 x + x2 = 31.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 31.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 31.5 + 0.25 Combine like terms: 31.5 + 0.25 = 31.75 1.25 + x2 = 31.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (x + 0.5) equal to 5.634713835 and -5.634713835.Subproblem 1
x + 0.5 = 5.634713835 Simplifying x + 0.5 = 5.634713835 Reorder the terms: 0.5 + x = 5.634713835 Solving 0.5 + x = 5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.634713835 + -0.5 x = 5.634713835 + -0.5 Combine like terms: 5.634713835 + -0.5 = 5.134713835 x = 5.134713835 Simplifying x = 5.134713835Subproblem 2
x + 0.5 = -5.634713835 Simplifying x + 0.5 = -5.634713835 Reorder the terms: 0.5 + x = -5.634713835 Solving 0.5 + x = -5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.634713835 + -0.5 x = -5.634713835 + -0.5 Combine like terms: -5.634713835 + -0.5 = -6.134713835 x = -6.134713835 Simplifying x = -6.134713835Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.134713835, -6.134713835}Solution
x = {5.134713835, -6.134713835}
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