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Simplifying 32x2 + -332x + 8 = 0 Reorder the terms: 8 + -332x + 32x2 = 0 Solving 8 + -332x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -83x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -83x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + -83x + 8x2 = 0 Solving 2 + -83x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -10.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -10.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -10.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -10.375x + x2 = 0 + -0.25 -10.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -10.375x + x2 = -0.25 The x term is -10.375x. Take half its coefficient (-5.1875). Square it (26.91015625) and add it to both sides. Add '26.91015625' to each side of the equation. -10.375x + 26.91015625 + x2 = -0.25 + 26.91015625 Reorder the terms: 26.91015625 + -10.375x + x2 = -0.25 + 26.91015625 Combine like terms: -0.25 + 26.91015625 = 26.66015625 26.91015625 + -10.375x + x2 = 26.66015625 Factor a perfect square on the left side: (x + -5.1875)(x + -5.1875) = 26.66015625 Calculate the square root of the right side: 5.163347388 Break this problem into two subproblems by setting (x + -5.1875) equal to 5.163347388 and -5.163347388.Subproblem 1
x + -5.1875 = 5.163347388 Simplifying x + -5.1875 = 5.163347388 Reorder the terms: -5.1875 + x = 5.163347388 Solving -5.1875 + x = 5.163347388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1875' to each side of the equation. -5.1875 + 5.1875 + x = 5.163347388 + 5.1875 Combine like terms: -5.1875 + 5.1875 = 0.0000 0.0000 + x = 5.163347388 + 5.1875 x = 5.163347388 + 5.1875 Combine like terms: 5.163347388 + 5.1875 = 10.350847388 x = 10.350847388 Simplifying x = 10.350847388Subproblem 2
x + -5.1875 = -5.163347388 Simplifying x + -5.1875 = -5.163347388 Reorder the terms: -5.1875 + x = -5.163347388 Solving -5.1875 + x = -5.163347388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.1875' to each side of the equation. -5.1875 + 5.1875 + x = -5.163347388 + 5.1875 Combine like terms: -5.1875 + 5.1875 = 0.0000 0.0000 + x = -5.163347388 + 5.1875 x = -5.163347388 + 5.1875 Combine like terms: -5.163347388 + 5.1875 = 0.024152612 x = 0.024152612 Simplifying x = 0.024152612Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.350847388, 0.024152612}Solution
x = {10.350847388, 0.024152612}
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