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Simplifying (10x + -20)(x + 35) = 180 Reorder the terms: (-20 + 10x)(x + 35) = 180 Reorder the terms: (-20 + 10x)(35 + x) = 180 Multiply (-20 + 10x) * (35 + x) (-20(35 + x) + 10x * (35 + x)) = 180 ((35 * -20 + x * -20) + 10x * (35 + x)) = 180 ((-700 + -20x) + 10x * (35 + x)) = 180 (-700 + -20x + (35 * 10x + x * 10x)) = 180 (-700 + -20x + (350x + 10x2)) = 180 Combine like terms: -20x + 350x = 330x (-700 + 330x + 10x2) = 180 Solving -700 + 330x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -700 + -180 + 330x + 10x2 = 180 + -180 Combine like terms: -700 + -180 = -880 -880 + 330x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -880 + 330x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-88 + 33x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-88 + 33x + x2)' equal to zero and attempt to solve: Simplifying -88 + 33x + x2 = 0 Solving -88 + 33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 33x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 33x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 33x + x2 = 0 + 88 33x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 33x + x2 = 88 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = 88 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 88 + 272.25 Combine like terms: 88 + 272.25 = 360.25 272.25 + 33x + x2 = 360.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 360.25 Calculate the square root of the right side: 18.980252896 Break this problem into two subproblems by setting (x + 16.5) equal to 18.980252896 and -18.980252896.Subproblem 1
x + 16.5 = 18.980252896 Simplifying x + 16.5 = 18.980252896 Reorder the terms: 16.5 + x = 18.980252896 Solving 16.5 + x = 18.980252896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 18.980252896 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 18.980252896 + -16.5 x = 18.980252896 + -16.5 Combine like terms: 18.980252896 + -16.5 = 2.480252896 x = 2.480252896 Simplifying x = 2.480252896Subproblem 2
x + 16.5 = -18.980252896 Simplifying x + 16.5 = -18.980252896 Reorder the terms: 16.5 + x = -18.980252896 Solving 16.5 + x = -18.980252896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -18.980252896 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -18.980252896 + -16.5 x = -18.980252896 + -16.5 Combine like terms: -18.980252896 + -16.5 = -35.480252896 x = -35.480252896 Simplifying x = -35.480252896Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.480252896, -35.480252896}Solution
x = {2.480252896, -35.480252896}
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