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Simplifying 2x2 + 20x = 180 Reorder the terms: 20x + 2x2 = 180 Solving 20x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 20x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 10x + x2)' equal to zero and attempt to solve: Simplifying -90 + 10x + x2 = 0 Solving -90 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 10x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 10x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 10x + x2 = 0 + 90 10x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 10x + x2 = 90 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 90 + 25 Reorder the terms: 25 + 10x + x2 = 90 + 25 Combine like terms: 90 + 25 = 115 25 + 10x + x2 = 115 Factor a perfect square on the left side: (x + 5)(x + 5) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 5) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 5 = 10.723805295 Simplifying x + 5 = 10.723805295 Reorder the terms: 5 + x = 10.723805295 Solving 5 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 10.723805295 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.723805295 + -5 x = 10.723805295 + -5 Combine like terms: 10.723805295 + -5 = 5.723805295 x = 5.723805295 Simplifying x = 5.723805295Subproblem 2
x + 5 = -10.723805295 Simplifying x + 5 = -10.723805295 Reorder the terms: 5 + x = -10.723805295 Solving 5 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -10.723805295 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.723805295 + -5 x = -10.723805295 + -5 Combine like terms: -10.723805295 + -5 = -15.723805295 x = -15.723805295 Simplifying x = -15.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.723805295, -15.723805295}Solution
x = {5.723805295, -15.723805295}
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