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Simplifying 14 = 32x + -1(x * x) Multiply x * x 14 = 32x + -1(x2) Solving 14 = 32x + -1x2 Solving for variable 'x'. Reorder the terms: 14 + -32x + x2 = 32x + -32x + -1x2 + x2 Combine like terms: 32x + -32x = 0 14 + -32x + x2 = 0 + -1x2 + x2 14 + -32x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 14 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -32x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -32x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -32x + x2 = 0 + -14 -32x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -32x + x2 = -14 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -14 + 256 Reorder the terms: 256 + -32x + x2 = -14 + 256 Combine like terms: -14 + 256 = 242 256 + -32x + x2 = 242 Factor a perfect square on the left side: (x + -16)(x + -16) = 242 Calculate the square root of the right side: 15.556349186 Break this problem into two subproblems by setting (x + -16) equal to 15.556349186 and -15.556349186.Subproblem 1
x + -16 = 15.556349186 Simplifying x + -16 = 15.556349186 Reorder the terms: -16 + x = 15.556349186 Solving -16 + x = 15.556349186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 15.556349186 + 16 Combine like terms: -16 + 16 = 0 0 + x = 15.556349186 + 16 x = 15.556349186 + 16 Combine like terms: 15.556349186 + 16 = 31.556349186 x = 31.556349186 Simplifying x = 31.556349186Subproblem 2
x + -16 = -15.556349186 Simplifying x + -16 = -15.556349186 Reorder the terms: -16 + x = -15.556349186 Solving -16 + x = -15.556349186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -15.556349186 + 16 Combine like terms: -16 + 16 = 0 0 + x = -15.556349186 + 16 x = -15.556349186 + 16 Combine like terms: -15.556349186 + 16 = 0.443650814 x = 0.443650814 Simplifying x = 0.443650814Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.556349186, 0.443650814}
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