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Simplifying 4x + 29 = x2 + -12x + 31 Reorder the terms: 29 + 4x = x2 + -12x + 31 Reorder the terms: 29 + 4x = 31 + -12x + x2 Solving 29 + 4x = 31 + -12x + x2 Solving for variable 'x'. Reorder the terms: 29 + -31 + 4x + 12x + -1x2 = 31 + -12x + x2 + -31 + 12x + -1x2 Combine like terms: 29 + -31 = -2 -2 + 4x + 12x + -1x2 = 31 + -12x + x2 + -31 + 12x + -1x2 Combine like terms: 4x + 12x = 16x -2 + 16x + -1x2 = 31 + -12x + x2 + -31 + 12x + -1x2 Reorder the terms: -2 + 16x + -1x2 = 31 + -31 + -12x + 12x + x2 + -1x2 Combine like terms: 31 + -31 = 0 -2 + 16x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -2 + 16x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -2 + 16x + -1x2 = 0 + x2 + -1x2 -2 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -16x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -16x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -16x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -16x + x2 = 0 + -2 -16x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -16x + x2 = -2 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 = -2 + 64 Reorder the terms: 64 + -16x + x2 = -2 + 64 Combine like terms: -2 + 64 = 62 64 + -16x + x2 = 62 Factor a perfect square on the left side: (x + -8)(x + -8) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -8) equal to 7.874007874 and -7.874007874.Subproblem 1
x + -8 = 7.874007874 Simplifying x + -8 = 7.874007874 Reorder the terms: -8 + x = 7.874007874 Solving -8 + x = 7.874007874 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 = 7.874007874 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.874007874 + 8 x = 7.874007874 + 8 Combine like terms: 7.874007874 + 8 = 15.874007874 x = 15.874007874 Simplifying x = 15.874007874Subproblem 2
x + -8 = -7.874007874 Simplifying x + -8 = -7.874007874 Reorder the terms: -8 + x = -7.874007874 Solving -8 + x = -7.874007874 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 = -7.874007874 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.874007874 + 8 x = -7.874007874 + 8 Combine like terms: -7.874007874 + 8 = 0.125992126 x = 0.125992126 Simplifying x = 0.125992126Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.874007874, 0.125992126}
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