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Simplifying (4x + -52)(2x + -18) = 180 Reorder the terms: (-52 + 4x)(2x + -18) = 180 Reorder the terms: (-52 + 4x)(-18 + 2x) = 180 Multiply (-52 + 4x) * (-18 + 2x) (-52(-18 + 2x) + 4x * (-18 + 2x)) = 180 ((-18 * -52 + 2x * -52) + 4x * (-18 + 2x)) = 180 ((936 + -104x) + 4x * (-18 + 2x)) = 180 (936 + -104x + (-18 * 4x + 2x * 4x)) = 180 (936 + -104x + (-72x + 8x2)) = 180 Combine like terms: -104x + -72x = -176x (936 + -176x + 8x2) = 180 Solving 936 + -176x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: 936 + -180 + -176x + 8x2 = 180 + -180 Combine like terms: 936 + -180 = 756 756 + -176x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 756 + -176x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(189 + -44x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(189 + -44x + 2x2)' equal to zero and attempt to solve: Simplifying 189 + -44x + 2x2 = 0 Solving 189 + -44x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 94.5 + -22x + x2 = 0 Move the constant term to the right: Add '-94.5' to each side of the equation. 94.5 + -22x + -94.5 + x2 = 0 + -94.5 Reorder the terms: 94.5 + -94.5 + -22x + x2 = 0 + -94.5 Combine like terms: 94.5 + -94.5 = 0.0 0.0 + -22x + x2 = 0 + -94.5 -22x + x2 = 0 + -94.5 Combine like terms: 0 + -94.5 = -94.5 -22x + x2 = -94.5 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -94.5 + 121 Reorder the terms: 121 + -22x + x2 = -94.5 + 121 Combine like terms: -94.5 + 121 = 26.5 121 + -22x + x2 = 26.5 Factor a perfect square on the left side: (x + -11)(x + -11) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + -11) equal to 5.14781507 and -5.14781507.Subproblem 1
x + -11 = 5.14781507 Simplifying x + -11 = 5.14781507 Reorder the terms: -11 + x = 5.14781507 Solving -11 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 5.14781507 + 11 Combine like terms: -11 + 11 = 0 0 + x = 5.14781507 + 11 x = 5.14781507 + 11 Combine like terms: 5.14781507 + 11 = 16.14781507 x = 16.14781507 Simplifying x = 16.14781507Subproblem 2
x + -11 = -5.14781507 Simplifying x + -11 = -5.14781507 Reorder the terms: -11 + x = -5.14781507 Solving -11 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -5.14781507 + 11 Combine like terms: -11 + 11 = 0 0 + x = -5.14781507 + 11 x = -5.14781507 + 11 Combine like terms: -5.14781507 + 11 = 5.85218493 x = 5.85218493 Simplifying x = 5.85218493Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.14781507, 5.85218493}Solution
x = {16.14781507, 5.85218493}
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