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Simplifying x(x + 16) = (x + 8) * 2 Reorder the terms: x(16 + x) = (x + 8) * 2 (16 * x + x * x) = (x + 8) * 2 (16x + x2) = (x + 8) * 2 Reorder the terms: 16x + x2 = (8 + x) * 2 Reorder the terms for easier multiplication: 16x + x2 = 2(8 + x) 16x + x2 = (8 * 2 + x * 2) 16x + x2 = (16 + 2x) Solving 16x + x2 = 16 + 2x Solving for variable 'x'. Reorder the terms: -16 + 16x + -2x + x2 = 16 + 2x + -16 + -2x Combine like terms: 16x + -2x = 14x -16 + 14x + x2 = 16 + 2x + -16 + -2x Reorder the terms: -16 + 14x + x2 = 16 + -16 + 2x + -2x Combine like terms: 16 + -16 = 0 -16 + 14x + x2 = 0 + 2x + -2x -16 + 14x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -16 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 14x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 14x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 14x + x2 = 0 + 16 14x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 14x + x2 = 16 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 16 + 49 Reorder the terms: 49 + 14x + x2 = 16 + 49 Combine like terms: 16 + 49 = 65 49 + 14x + x2 = 65 Factor a perfect square on the left side: (x + 7)(x + 7) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 7) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 7 = 8.062257748 Simplifying x + 7 = 8.062257748 Reorder the terms: 7 + x = 8.062257748 Solving 7 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 8.062257748 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.062257748 + -7 x = 8.062257748 + -7 Combine like terms: 8.062257748 + -7 = 1.062257748 x = 1.062257748 Simplifying x = 1.062257748Subproblem 2
x + 7 = -8.062257748 Simplifying x + 7 = -8.062257748 Reorder the terms: 7 + x = -8.062257748 Solving 7 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -8.062257748 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.062257748 + -7 x = -8.062257748 + -7 Combine like terms: -8.062257748 + -7 = -15.062257748 x = -15.062257748 Simplifying x = -15.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.062257748, -15.062257748}
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