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Simplifying x2 + 36 = 2x2 + 16x + 31 Reorder the terms: 36 + x2 = 2x2 + 16x + 31 Reorder the terms: 36 + x2 = 31 + 16x + 2x2 Solving 36 + x2 = 31 + 16x + 2x2 Solving for variable 'x'. Reorder the terms: 36 + -31 + -16x + x2 + -2x2 = 31 + 16x + 2x2 + -31 + -16x + -2x2 Combine like terms: 36 + -31 = 5 5 + -16x + x2 + -2x2 = 31 + 16x + 2x2 + -31 + -16x + -2x2 Combine like terms: x2 + -2x2 = -1x2 5 + -16x + -1x2 = 31 + 16x + 2x2 + -31 + -16x + -2x2 Reorder the terms: 5 + -16x + -1x2 = 31 + -31 + 16x + -16x + 2x2 + -2x2 Combine like terms: 31 + -31 = 0 5 + -16x + -1x2 = 0 + 16x + -16x + 2x2 + -2x2 5 + -16x + -1x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 5 + -16x + -1x2 = 0 + 2x2 + -2x2 5 + -16x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 16x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 16x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 16x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 16x + x2 = 0 + 5 16x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 16x + x2 = 5 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 = 5 + 64 Reorder the terms: 64 + 16x + x2 = 5 + 64 Combine like terms: 5 + 64 = 69 64 + 16x + x2 = 69 Factor a perfect square on the left side: (x + 8)(x + 8) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 8) equal to 8.306623863 and -8.306623863.Subproblem 1
x + 8 = 8.306623863 Simplifying x + 8 = 8.306623863 Reorder the terms: 8 + x = 8.306623863 Solving 8 + x = 8.306623863 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 = 8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.306623863 + -8 x = 8.306623863 + -8 Combine like terms: 8.306623863 + -8 = 0.306623863 x = 0.306623863 Simplifying x = 0.306623863Subproblem 2
x + 8 = -8.306623863 Simplifying x + 8 = -8.306623863 Reorder the terms: 8 + x = -8.306623863 Solving 8 + x = -8.306623863 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 = -8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.306623863 + -8 x = -8.306623863 + -8 Combine like terms: -8.306623863 + -8 = -16.306623863 x = -16.306623863 Simplifying x = -16.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306623863, -16.306623863}
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