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Simplifying (2x + 6)(x + -1) = 176 Reorder the terms: (6 + 2x)(x + -1) = 176 Reorder the terms: (6 + 2x)(-1 + x) = 176 Multiply (6 + 2x) * (-1 + x) (6(-1 + x) + 2x * (-1 + x)) = 176 ((-1 * 6 + x * 6) + 2x * (-1 + x)) = 176 ((-6 + 6x) + 2x * (-1 + x)) = 176 (-6 + 6x + (-1 * 2x + x * 2x)) = 176 (-6 + 6x + (-2x + 2x2)) = 176 Combine like terms: 6x + -2x = 4x (-6 + 4x + 2x2) = 176 Solving -6 + 4x + 2x2 = 176 Solving for variable 'x'. Reorder the terms: -6 + -176 + 4x + 2x2 = 176 + -176 Combine like terms: -6 + -176 = -182 -182 + 4x + 2x2 = 176 + -176 Combine like terms: 176 + -176 = 0 -182 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-91 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-91 + 2x + x2)' equal to zero and attempt to solve: Simplifying -91 + 2x + x2 = 0 Solving -91 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 2x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 2x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 2x + x2 = 0 + 91 2x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 2x + x2 = 91 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 91 + 1 Reorder the terms: 1 + 2x + x2 = 91 + 1 Combine like terms: 91 + 1 = 92 1 + 2x + x2 = 92 Factor a perfect square on the left side: (x + 1)(x + 1) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + 1) equal to 9.591663047 and -9.591663047.Subproblem 1
x + 1 = 9.591663047 Simplifying x + 1 = 9.591663047 Reorder the terms: 1 + x = 9.591663047 Solving 1 + x = 9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.591663047 + -1 x = 9.591663047 + -1 Combine like terms: 9.591663047 + -1 = 8.591663047 x = 8.591663047 Simplifying x = 8.591663047Subproblem 2
x + 1 = -9.591663047 Simplifying x + 1 = -9.591663047 Reorder the terms: 1 + x = -9.591663047 Solving 1 + x = -9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.591663047 + -1 x = -9.591663047 + -1 Combine like terms: -9.591663047 + -1 = -10.591663047 x = -10.591663047 Simplifying x = -10.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.591663047, -10.591663047}Solution
x = {8.591663047, -10.591663047}
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