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Simplifying x2 = 16x + -13 Reorder the terms: x2 = -13 + 16x Solving x2 = -13 + 16x Solving for variable 'x'. Reorder the terms: 13 + -16x + x2 = -13 + 16x + 13 + -16x Reorder the terms: 13 + -16x + x2 = -13 + 13 + 16x + -16x Combine like terms: -13 + 13 = 0 13 + -16x + x2 = 0 + 16x + -16x 13 + -16x + x2 = 16x + -16x Combine like terms: 16x + -16x = 0 13 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -16x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -16x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -16x + x2 = 0 + -13 -16x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -16x + x2 = -13 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 = -13 + 64 Reorder the terms: 64 + -16x + x2 = -13 + 64 Combine like terms: -13 + 64 = 51 64 + -16x + x2 = 51 Factor a perfect square on the left side: (x + -8)(x + -8) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -8) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -8 = 7.141428429 Simplifying x + -8 = 7.141428429 Reorder the terms: -8 + x = 7.141428429 Solving -8 + x = 7.141428429 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 = 7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.141428429 + 8 x = 7.141428429 + 8 Combine like terms: 7.141428429 + 8 = 15.141428429 x = 15.141428429 Simplifying x = 15.141428429Subproblem 2
x + -8 = -7.141428429 Simplifying x + -8 = -7.141428429 Reorder the terms: -8 + x = -7.141428429 Solving -8 + x = -7.141428429 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 = -7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.141428429 + 8 x = -7.141428429 + 8 Combine like terms: -7.141428429 + 8 = 0.858571571 x = 0.858571571 Simplifying x = 0.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.141428429, 0.858571571}
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