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Simplifying 2x2 + -52x = 5x2 + -4x + -36 Reorder the terms: -52x + 2x2 = 5x2 + -4x + -36 Reorder the terms: -52x + 2x2 = -36 + -4x + 5x2 Solving -52x + 2x2 = -36 + -4x + 5x2 Solving for variable 'x'. Reorder the terms: 36 + -52x + 4x + 2x2 + -5x2 = -36 + -4x + 5x2 + 36 + 4x + -5x2 Combine like terms: -52x + 4x = -48x 36 + -48x + 2x2 + -5x2 = -36 + -4x + 5x2 + 36 + 4x + -5x2 Combine like terms: 2x2 + -5x2 = -3x2 36 + -48x + -3x2 = -36 + -4x + 5x2 + 36 + 4x + -5x2 Reorder the terms: 36 + -48x + -3x2 = -36 + 36 + -4x + 4x + 5x2 + -5x2 Combine like terms: -36 + 36 = 0 36 + -48x + -3x2 = 0 + -4x + 4x + 5x2 + -5x2 36 + -48x + -3x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 36 + -48x + -3x2 = 0 + 5x2 + -5x2 36 + -48x + -3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 36 + -48x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -16x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + -16x + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -16x + -1x2 = 0 Solving 12 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 16x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 16x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 16x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 16x + x2 = 0 + 12 16x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 16x + x2 = 12 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 12 + 64 Reorder the terms: 64 + 16x + x2 = 12 + 64 Combine like terms: 12 + 64 = 76 64 + 16x + x2 = 76 Factor a perfect square on the left side: (x + 8)(x + 8) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + 8) equal to 8.717797887 and -8.717797887.Subproblem 1
x + 8 = 8.717797887 Simplifying x + 8 = 8.717797887 Reorder the terms: 8 + x = 8.717797887 Solving 8 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.717797887 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.717797887 + -8 x = 8.717797887 + -8 Combine like terms: 8.717797887 + -8 = 0.717797887 x = 0.717797887 Simplifying x = 0.717797887Subproblem 2
x + 8 = -8.717797887 Simplifying x + 8 = -8.717797887 Reorder the terms: 8 + x = -8.717797887 Solving 8 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.717797887 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.717797887 + -8 x = -8.717797887 + -8 Combine like terms: -8.717797887 + -8 = -16.717797887 x = -16.717797887 Simplifying x = -16.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.717797887, -16.717797887}Solution
x = {0.717797887, -16.717797887}
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