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Simplifying (x + 4) * 2 = x(x + -14) + 5 Reorder the terms: (4 + x) * 2 = x(x + -14) + 5 Reorder the terms for easier multiplication: 2(4 + x) = x(x + -14) + 5 (4 * 2 + x * 2) = x(x + -14) + 5 (8 + 2x) = x(x + -14) + 5 Reorder the terms: 8 + 2x = x(-14 + x) + 5 8 + 2x = (-14 * x + x * x) + 5 8 + 2x = (-14x + x2) + 5 Reorder the terms: 8 + 2x = 5 + -14x + x2 Solving 8 + 2x = 5 + -14x + x2 Solving for variable 'x'. Reorder the terms: 8 + -5 + 2x + 14x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Combine like terms: 8 + -5 = 3 3 + 2x + 14x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Combine like terms: 2x + 14x = 16x 3 + 16x + -1x2 = 5 + -14x + x2 + -5 + 14x + -1x2 Reorder the terms: 3 + 16x + -1x2 = 5 + -5 + -14x + 14x + x2 + -1x2 Combine like terms: 5 + -5 = 0 3 + 16x + -1x2 = 0 + -14x + 14x + x2 + -1x2 3 + 16x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 3 + 16x + -1x2 = 0 + x2 + -1x2 3 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -16x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -16x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -16x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -16x + x2 = 0 + 3 -16x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -16x + x2 = 3 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 = 3 + 64 Reorder the terms: 64 + -16x + x2 = 3 + 64 Combine like terms: 3 + 64 = 67 64 + -16x + x2 = 67 Factor a perfect square on the left side: (x + -8)(x + -8) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -8) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -8 = 8.185352772 Simplifying x + -8 = 8.185352772 Reorder the terms: -8 + x = 8.185352772 Solving -8 + x = 8.185352772 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 = 8.185352772 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.185352772 + 8 x = 8.185352772 + 8 Combine like terms: 8.185352772 + 8 = 16.185352772 x = 16.185352772 Simplifying x = 16.185352772Subproblem 2
x + -8 = -8.185352772 Simplifying x + -8 = -8.185352772 Reorder the terms: -8 + x = -8.185352772 Solving -8 + x = -8.185352772 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 = -8.185352772 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.185352772 + 8 x = -8.185352772 + 8 Combine like terms: -8.185352772 + 8 = -0.185352772 x = -0.185352772 Simplifying x = -0.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.185352772, -0.185352772}
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