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Simplifying (x + 5)(2x + -2) = 154 Reorder the terms: (5 + x)(2x + -2) = 154 Reorder the terms: (5 + x)(-2 + 2x) = 154 Multiply (5 + x) * (-2 + 2x) (5(-2 + 2x) + x(-2 + 2x)) = 154 ((-2 * 5 + 2x * 5) + x(-2 + 2x)) = 154 ((-10 + 10x) + x(-2 + 2x)) = 154 (-10 + 10x + (-2 * x + 2x * x)) = 154 (-10 + 10x + (-2x + 2x2)) = 154 Combine like terms: 10x + -2x = 8x (-10 + 8x + 2x2) = 154 Solving -10 + 8x + 2x2 = 154 Solving for variable 'x'. Reorder the terms: -10 + -154 + 8x + 2x2 = 154 + -154 Combine like terms: -10 + -154 = -164 -164 + 8x + 2x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -164 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-82 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-82 + 4x + x2)' equal to zero and attempt to solve: Simplifying -82 + 4x + x2 = 0 Solving -82 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 4x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 4x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 4x + x2 = 0 + 82 4x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 4x + x2 = 82 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 82 + 4 Reorder the terms: 4 + 4x + x2 = 82 + 4 Combine like terms: 82 + 4 = 86 4 + 4x + x2 = 86 Factor a perfect square on the left side: (x + 2)(x + 2) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 2) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 2 = 9.273618495 Simplifying x + 2 = 9.273618495 Reorder the terms: 2 + x = 9.273618495 Solving 2 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.273618495 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.273618495 + -2 x = 9.273618495 + -2 Combine like terms: 9.273618495 + -2 = 7.273618495 x = 7.273618495 Simplifying x = 7.273618495Subproblem 2
x + 2 = -9.273618495 Simplifying x + 2 = -9.273618495 Reorder the terms: 2 + x = -9.273618495 Solving 2 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.273618495 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.273618495 + -2 x = -9.273618495 + -2 Combine like terms: -9.273618495 + -2 = -11.273618495 x = -11.273618495 Simplifying x = -11.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.273618495, -11.273618495}Solution
x = {7.273618495, -11.273618495}
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