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Simplifying x2 = 12 + 16x Solving x2 = 12 + 16x Solving for variable 'x'. Reorder the terms: -12 + -16x + x2 = 12 + 16x + -12 + -16x Reorder the terms: -12 + -16x + x2 = 12 + -12 + 16x + -16x Combine like terms: 12 + -12 = 0 -12 + -16x + x2 = 0 + 16x + -16x -12 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -12 + -16x + x2 = 0 Begin completing the square. 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 = 16.717797887 x = 16.717797887 Simplifying x = 16.717797887Subproblem 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 = -0.717797887 x = -0.717797887 Simplifying x = -0.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.717797887, -0.717797887}
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