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Simplifying x2 + 16x = 61 Reorder the terms: 16x + x2 = 61 Solving 16x + x2 = 61 Solving for variable 'x'. Reorder the terms: -61 + 16x + x2 = 61 + -61 Combine like terms: 61 + -61 = 0 -61 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 16x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 16x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 16x + x2 = 0 + 61 16x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 16x + x2 = 61 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 = 61 + 64 Reorder the terms: 64 + 16x + x2 = 61 + 64 Combine like terms: 61 + 64 = 125 64 + 16x + x2 = 125 Factor a perfect square on the left side: (x + 8)(x + 8) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 8) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 8 = 11.180339887 Simplifying x + 8 = 11.180339887 Reorder the terms: 8 + x = 11.180339887 Solving 8 + x = 11.180339887 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 = 11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.180339887 + -8 x = 11.180339887 + -8 Combine like terms: 11.180339887 + -8 = 3.180339887 x = 3.180339887 Simplifying x = 3.180339887Subproblem 2
x + 8 = -11.180339887 Simplifying x + 8 = -11.180339887 Reorder the terms: 8 + x = -11.180339887 Solving 8 + x = -11.180339887 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 = -11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.180339887 + -8 x = -11.180339887 + -8 Combine like terms: -11.180339887 + -8 = -19.180339887 x = -19.180339887 Simplifying x = -19.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.180339887, -19.180339887}
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