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Simplifying (2x + -2)(2x + -2) = 56 Reorder the terms: (-2 + 2x)(2x + -2) = 56 Reorder the terms: (-2 + 2x)(-2 + 2x) = 56 Multiply (-2 + 2x) * (-2 + 2x) (-2(-2 + 2x) + 2x * (-2 + 2x)) = 56 ((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) = 56 ((4 + -4x) + 2x * (-2 + 2x)) = 56 (4 + -4x + (-2 * 2x + 2x * 2x)) = 56 (4 + -4x + (-4x + 4x2)) = 56 Combine like terms: -4x + -4x = -8x (4 + -8x + 4x2) = 56 Solving 4 + -8x + 4x2 = 56 Solving for variable 'x'. Reorder the terms: 4 + -56 + -8x + 4x2 = 56 + -56 Combine like terms: 4 + -56 = -52 -52 + -8x + 4x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -52 + -8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + -2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + -2x + x2)' equal to zero and attempt to solve: Simplifying -13 + -2x + x2 = 0 Solving -13 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -2x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -2x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x + x2 = 0 + 13 -2x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2x + x2 = 13 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 = 13 + 1 Reorder the terms: 1 + -2x + x2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2x + x2 = 14 Factor a perfect square on the left side: (x + -1)(x + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -1 = 3.741657387 Simplifying x + -1 = 3.741657387 Reorder the terms: -1 + x = 3.741657387 Solving -1 + x = 3.741657387 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 = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.741657387 + 1 x = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 x = 4.741657387 Simplifying x = 4.741657387Subproblem 2
x + -1 = -3.741657387 Simplifying x + -1 = -3.741657387 Reorder the terms: -1 + x = -3.741657387 Solving -1 + x = -3.741657387 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 = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.741657387 + 1 x = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 x = -2.741657387 Simplifying x = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.741657387, -2.741657387}Solution
x = {4.741657387, -2.741657387}
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