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Simplifying 2(x + 3)(x + -1) = x + 176 Reorder the terms: 2(3 + x)(x + -1) = x + 176 Reorder the terms: 2(3 + x)(-1 + x) = x + 176 Multiply (3 + x) * (-1 + x) 2(3(-1 + x) + x(-1 + x)) = x + 176 2((-1 * 3 + x * 3) + x(-1 + x)) = x + 176 2((-3 + 3x) + x(-1 + x)) = x + 176 2(-3 + 3x + (-1 * x + x * x)) = x + 176 2(-3 + 3x + (-1x + x2)) = x + 176 Combine like terms: 3x + -1x = 2x 2(-3 + 2x + x2) = x + 176 (-3 * 2 + 2x * 2 + x2 * 2) = x + 176 (-6 + 4x + 2x2) = x + 176 Reorder the terms: -6 + 4x + 2x2 = 176 + x Solving -6 + 4x + 2x2 = 176 + x Solving for variable 'x'. Reorder the terms: -6 + -176 + 4x + -1x + 2x2 = 176 + x + -176 + -1x Combine like terms: -6 + -176 = -182 -182 + 4x + -1x + 2x2 = 176 + x + -176 + -1x Combine like terms: 4x + -1x = 3x -182 + 3x + 2x2 = 176 + x + -176 + -1x Reorder the terms: -182 + 3x + 2x2 = 176 + -176 + x + -1x Combine like terms: 176 + -176 = 0 -182 + 3x + 2x2 = 0 + x + -1x -182 + 3x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -182 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -91 + 1.5x + x2 = 0 Move the constant term to the right: Add '91' to each side of the equation. -91 + 1.5x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 1.5x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 1.5x + x2 = 0 + 91 1.5x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 1.5x + x2 = 91 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 91 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 91 + 0.5625 Combine like terms: 91 + 0.5625 = 91.5625 0.5625 + 1.5x + x2 = 91.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 91.5625 Calculate the square root of the right side: 9.568829605 Break this problem into two subproblems by setting (x + 0.75) equal to 9.568829605 and -9.568829605.Subproblem 1
x + 0.75 = 9.568829605 Simplifying x + 0.75 = 9.568829605 Reorder the terms: 0.75 + x = 9.568829605 Solving 0.75 + x = 9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.568829605 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.568829605 + -0.75 x = 9.568829605 + -0.75 Combine like terms: 9.568829605 + -0.75 = 8.818829605 x = 8.818829605 Simplifying x = 8.818829605Subproblem 2
x + 0.75 = -9.568829605 Simplifying x + 0.75 = -9.568829605 Reorder the terms: 0.75 + x = -9.568829605 Solving 0.75 + x = -9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.568829605 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.568829605 + -0.75 x = -9.568829605 + -0.75 Combine like terms: -9.568829605 + -0.75 = -10.318829605 x = -10.318829605 Simplifying x = -10.318829605Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.818829605, -10.318829605}
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