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Simplifying (x + 8)(x + -2) = 100 Reorder the terms: (8 + x)(x + -2) = 100 Reorder the terms: (8 + x)(-2 + x) = 100 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = 100 ((-2 * 8 + x * 8) + x(-2 + x)) = 100 ((-16 + 8x) + x(-2 + x)) = 100 (-16 + 8x + (-2 * x + x * x)) = 100 (-16 + 8x + (-2x + x2)) = 100 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = 100 Solving -16 + 6x + x2 = 100 Solving for variable 'x'. Reorder the terms: -16 + -100 + 6x + x2 = 100 + -100 Combine like terms: -16 + -100 = -116 -116 + 6x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -116 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 6x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 6x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 6x + x2 = 0 + 116 6x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 6x + x2 = 116 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 116 + 9 Reorder the terms: 9 + 6x + x2 = 116 + 9 Combine like terms: 116 + 9 = 125 9 + 6x + x2 = 125 Factor a perfect square on the left side: (x + 3)(x + 3) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 3) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 3 = 11.180339887 Simplifying x + 3 = 11.180339887 Reorder the terms: 3 + x = 11.180339887 Solving 3 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.180339887 + -3 x = 11.180339887 + -3 Combine like terms: 11.180339887 + -3 = 8.180339887 x = 8.180339887 Simplifying x = 8.180339887Subproblem 2
x + 3 = -11.180339887 Simplifying x + 3 = -11.180339887 Reorder the terms: 3 + x = -11.180339887 Solving 3 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.180339887 + -3 x = -11.180339887 + -3 Combine like terms: -11.180339887 + -3 = -14.180339887 x = -14.180339887 Simplifying x = -14.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.180339887, -14.180339887}
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