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Simplifying 2x(x + -20) = 180 Reorder the terms: 2x(-20 + x) = 180 (-20 * 2x + x * 2x) = 180 (-40x + 2x2) = 180 Solving -40x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -40x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -20x + x2)' equal to zero and attempt to solve: Simplifying -90 + -20x + x2 = 0 Solving -90 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -20x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -20x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -20x + x2 = 0 + 90 -20x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -20x + x2 = 90 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 90 + 100 Reorder the terms: 100 + -20x + x2 = 90 + 100 Combine like terms: 90 + 100 = 190 100 + -20x + x2 = 190 Factor a perfect square on the left side: (x + -10)(x + -10) = 190 Calculate the square root of the right side: 13.784048752 Break this problem into two subproblems by setting (x + -10) equal to 13.784048752 and -13.784048752.Subproblem 1
x + -10 = 13.784048752 Simplifying x + -10 = 13.784048752 Reorder the terms: -10 + x = 13.784048752 Solving -10 + x = 13.784048752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 13.784048752 + 10 Combine like terms: -10 + 10 = 0 0 + x = 13.784048752 + 10 x = 13.784048752 + 10 Combine like terms: 13.784048752 + 10 = 23.784048752 x = 23.784048752 Simplifying x = 23.784048752Subproblem 2
x + -10 = -13.784048752 Simplifying x + -10 = -13.784048752 Reorder the terms: -10 + x = -13.784048752 Solving -10 + x = -13.784048752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -13.784048752 + 10 Combine like terms: -10 + 10 = 0 0 + x = -13.784048752 + 10 x = -13.784048752 + 10 Combine like terms: -13.784048752 + 10 = -3.784048752 x = -3.784048752 Simplifying x = -3.784048752Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.784048752, -3.784048752}Solution
x = {23.784048752, -3.784048752}
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