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Simplifying (x + -7)(x + -5) = 182 Reorder the terms: (-7 + x)(x + -5) = 182 Reorder the terms: (-7 + x)(-5 + x) = 182 Multiply (-7 + x) * (-5 + x) (-7(-5 + x) + x(-5 + x)) = 182 ((-5 * -7 + x * -7) + x(-5 + x)) = 182 ((35 + -7x) + x(-5 + x)) = 182 (35 + -7x + (-5 * x + x * x)) = 182 (35 + -7x + (-5x + x2)) = 182 Combine like terms: -7x + -5x = -12x (35 + -12x + x2) = 182 Solving 35 + -12x + x2 = 182 Solving for variable 'x'. Reorder the terms: 35 + -182 + -12x + x2 = 182 + -182 Combine like terms: 35 + -182 = -147 -147 + -12x + x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -147 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + -12x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + -12x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + -12x + x2 = 0 + 147 -12x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 -12x + x2 = 147 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 147 + 36 Reorder the terms: 36 + -12x + x2 = 147 + 36 Combine like terms: 147 + 36 = 183 36 + -12x + x2 = 183 Factor a perfect square on the left side: (x + -6)(x + -6) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (x + -6) equal to 13.527749258 and -13.527749258.Subproblem 1
x + -6 = 13.527749258 Simplifying x + -6 = 13.527749258 Reorder the terms: -6 + x = 13.527749258 Solving -6 + x = 13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 13.527749258 + 6 Combine like terms: -6 + 6 = 0 0 + x = 13.527749258 + 6 x = 13.527749258 + 6 Combine like terms: 13.527749258 + 6 = 19.527749258 x = 19.527749258 Simplifying x = 19.527749258Subproblem 2
x + -6 = -13.527749258 Simplifying x + -6 = -13.527749258 Reorder the terms: -6 + x = -13.527749258 Solving -6 + x = -13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -13.527749258 + 6 Combine like terms: -6 + 6 = 0 0 + x = -13.527749258 + 6 x = -13.527749258 + 6 Combine like terms: -13.527749258 + 6 = -7.527749258 x = -7.527749258 Simplifying x = -7.527749258Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.527749258, -7.527749258}
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