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Simplifying (x + -8)(x + -8) + -14 = 0 Reorder the terms: (-8 + x)(x + -8) + -14 = 0 Reorder the terms: (-8 + x)(-8 + x) + -14 = 0 Multiply (-8 + x) * (-8 + x) (-8(-8 + x) + x(-8 + x)) + -14 = 0 ((-8 * -8 + x * -8) + x(-8 + x)) + -14 = 0 ((64 + -8x) + x(-8 + x)) + -14 = 0 (64 + -8x + (-8 * x + x * x)) + -14 = 0 (64 + -8x + (-8x + x2)) + -14 = 0 Combine like terms: -8x + -8x = -16x (64 + -16x + x2) + -14 = 0 Reorder the terms: 64 + -14 + -16x + x2 = 0 Combine like terms: 64 + -14 = 50 50 + -16x + x2 = 0 Solving 50 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -16x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -16x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -16x + x2 = 0 + -50 -16x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -16x + x2 = -50 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 = -50 + 64 Reorder the terms: 64 + -16x + x2 = -50 + 64 Combine like terms: -50 + 64 = 14 64 + -16x + x2 = 14 Factor a perfect square on the left side: (x + -8)(x + -8) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -8) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -8 = 3.741657387 Simplifying x + -8 = 3.741657387 Reorder the terms: -8 + x = 3.741657387 Solving -8 + x = 3.741657387 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 = 3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.741657387 + 8 x = 3.741657387 + 8 Combine like terms: 3.741657387 + 8 = 11.741657387 x = 11.741657387 Simplifying x = 11.741657387Subproblem 2
x + -8 = -3.741657387 Simplifying x + -8 = -3.741657387 Reorder the terms: -8 + x = -3.741657387 Solving -8 + x = -3.741657387 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 = -3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.741657387 + 8 x = -3.741657387 + 8 Combine like terms: -3.741657387 + 8 = 4.258342613 x = 4.258342613 Simplifying x = 4.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.741657387, 4.258342613}
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