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Simplifying (x + -1)(x + 2) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 Reorder the terms: (-1 + x)(x + 2) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 Reorder the terms: (-1 + x)(2 + x) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 Multiply (-1 + x) * (2 + x) (-1(2 + x) + x(2 + x)) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 ((2 * -1 + x * -1) + x(2 + x)) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 ((-2 + -1x) + x(2 + x)) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 (-2 + -1x + (2 * x + x * x)) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 (-2 + -1x + (2x + x2)) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 Combine like terms: -1x + 2x = 1x (-2 + 1x + x2) + -1x(x + 3) = (x + -2)(x + 2) + -1(x + -1) * 178 Reorder the terms: -2 + 1x + x2 + -1x(3 + x) = (x + -2)(x + 2) + -1(x + -1) * 178 -2 + 1x + x2 + (3 * -1x + x * -1x) = (x + -2)(x + 2) + -1(x + -1) * 178 -2 + 1x + x2 + (-3x + -1x2) = (x + -2)(x + 2) + -1(x + -1) * 178 Reorder the terms: -2 + 1x + -3x + x2 + -1x2 = (x + -2)(x + 2) + -1(x + -1) * 178 Combine like terms: 1x + -3x = -2x -2 + -2x + x2 + -1x2 = (x + -2)(x + 2) + -1(x + -1) * 178 Combine like terms: x2 + -1x2 = 0 -2 + -2x + 0 = (x + -2)(x + 2) + -1(x + -1) * 178 -2 + -2x = (x + -2)(x + 2) + -1(x + -1) * 178 Reorder the terms: -2 + -2x = (-2 + x)(x + 2) + -1(x + -1) * 178 Reorder the terms: -2 + -2x = (-2 + x)(2 + x) + -1(x + -1) * 178 Multiply (-2 + x) * (2 + x) -2 + -2x = (-2(2 + x) + x(2 + x)) + -1(x + -1) * 178 -2 + -2x = ((2 * -2 + x * -2) + x(2 + x)) + -1(x + -1) * 178 -2 + -2x = ((-4 + -2x) + x(2 + x)) + -1(x + -1) * 178 -2 + -2x = (-4 + -2x + (2 * x + x * x)) + -1(x + -1) * 178 -2 + -2x = (-4 + -2x + (2x + x2)) + -1(x + -1) * 178 Combine like terms: -2x + 2x = 0 -2 + -2x = (-4 + 0 + x2) + -1(x + -1) * 178 -2 + -2x = (-4 + x2) + -1(x + -1) * 178 Reorder the terms: -2 + -2x = -4 + x2 + -1(-1 + x) * 178 Reorder the terms for easier multiplication: -2 + -2x = -4 + x2 + -1 * 178(-1 + x) Multiply -1 * 178 -2 + -2x = -4 + x2 + -178(-1 + x) -2 + -2x = -4 + x2 + (-1 * -178 + x * -178) -2 + -2x = -4 + x2 + (178 + -178x) Reorder the terms: -2 + -2x = -4 + 178 + -178x + x2 Combine like terms: -4 + 178 = 174 -2 + -2x = 174 + -178x + x2 Solving -2 + -2x = 174 + -178x + x2 Solving for variable 'x'. Reorder the terms: -2 + -174 + -2x + 178x + -1x2 = 174 + -178x + x2 + -174 + 178x + -1x2 Combine like terms: -2 + -174 = -176 -176 + -2x + 178x + -1x2 = 174 + -178x + x2 + -174 + 178x + -1x2 Combine like terms: -2x + 178x = 176x -176 + 176x + -1x2 = 174 + -178x + x2 + -174 + 178x + -1x2 Reorder the terms: -176 + 176x + -1x2 = 174 + -174 + -178x + 178x + x2 + -1x2 Combine like terms: 174 + -174 = 0 -176 + 176x + -1x2 = 0 + -178x + 178x + x2 + -1x2 -176 + 176x + -1x2 = -178x + 178x + x2 + -1x2 Combine like terms: -178x + 178x = 0 -176 + 176x + -1x2 = 0 + x2 + -1x2 -176 + 176x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -176 + 176x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 176 + -176x + x2 = 0 Move the constant term to the right: Add '-176' to each side of the equation. 176 + -176x + -176 + x2 = 0 + -176 Reorder the terms: 176 + -176 + -176x + x2 = 0 + -176 Combine like terms: 176 + -176 = 0 0 + -176x + x2 = 0 + -176 -176x + x2 = 0 + -176 Combine like terms: 0 + -176 = -176 -176x + x2 = -176 The x term is -176x. Take half its coefficient (-88). Square it (7744) and add it to both sides. Add '7744' to each side of the equation. -176x + 7744 + x2 = -176 + 7744 Reorder the terms: 7744 + -176x + x2 = -176 + 7744 Combine like terms: -176 + 7744 = 7568 7744 + -176x + x2 = 7568 Factor a perfect square on the left side: (x + -88)(x + -88) = 7568 Calculate the square root of the right side: 86.994252684 Break this problem into two subproblems by setting (x + -88) equal to 86.994252684 and -86.994252684.Subproblem 1
x + -88 = 86.994252684 Simplifying x + -88 = 86.994252684 Reorder the terms: -88 + x = 86.994252684 Solving -88 + x = 86.994252684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + x = 86.994252684 + 88 Combine like terms: -88 + 88 = 0 0 + x = 86.994252684 + 88 x = 86.994252684 + 88 Combine like terms: 86.994252684 + 88 = 174.994252684 x = 174.994252684 Simplifying x = 174.994252684Subproblem 2
x + -88 = -86.994252684 Simplifying x + -88 = -86.994252684 Reorder the terms: -88 + x = -86.994252684 Solving -88 + x = -86.994252684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + x = -86.994252684 + 88 Combine like terms: -88 + 88 = 0 0 + x = -86.994252684 + 88 x = -86.994252684 + 88 Combine like terms: -86.994252684 + 88 = 1.005747316 x = 1.005747316 Simplifying x = 1.005747316Solution
The solution to the problem is based on the solutions from the subproblems. x = {174.994252684, 1.005747316}
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