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Simplifying (2x + -4)(2x + -4) = 180 Reorder the terms: (-4 + 2x)(2x + -4) = 180 Reorder the terms: (-4 + 2x)(-4 + 2x) = 180 Multiply (-4 + 2x) * (-4 + 2x) (-4(-4 + 2x) + 2x * (-4 + 2x)) = 180 ((-4 * -4 + 2x * -4) + 2x * (-4 + 2x)) = 180 ((16 + -8x) + 2x * (-4 + 2x)) = 180 (16 + -8x + (-4 * 2x + 2x * 2x)) = 180 (16 + -8x + (-8x + 4x2)) = 180 Combine like terms: -8x + -8x = -16x (16 + -16x + 4x2) = 180 Solving 16 + -16x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 16 + -180 + -16x + 4x2 = 180 + -180 Combine like terms: 16 + -180 = -164 -164 + -16x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -164 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-41 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-41 + -4x + x2)' equal to zero and attempt to solve: Simplifying -41 + -4x + x2 = 0 Solving -41 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -4x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -4x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -4x + x2 = 0 + 41 -4x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -4x + x2 = 41 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 = 41 + 4 Reorder the terms: 4 + -4x + x2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + -4x + x2 = 45 Factor a perfect square on the left side: (x + -2)(x + -2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -2) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -2 = 6.708203933 Simplifying x + -2 = 6.708203933 Reorder the terms: -2 + x = 6.708203933 Solving -2 + x = 6.708203933 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 = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.708203933 + 2 x = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 x = 8.708203933 Simplifying x = 8.708203933Subproblem 2
x + -2 = -6.708203933 Simplifying x + -2 = -6.708203933 Reorder the terms: -2 + x = -6.708203933 Solving -2 + x = -6.708203933 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 = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.708203933 + 2 x = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 x = -4.708203933 Simplifying x = -4.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.708203933, -4.708203933}Solution
x = {8.708203933, -4.708203933}
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