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Simplifying 2x2 + -24x = 180 Reorder the terms: -24x + 2x2 = 180 Solving -24x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -24x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -12x + x2)' equal to zero and attempt to solve: Simplifying -90 + -12x + x2 = 0 Solving -90 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -12x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -12x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -12x + x2 = 0 + 90 -12x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -12x + x2 = 90 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 90 + 36 Reorder the terms: 36 + -12x + x2 = 90 + 36 Combine like terms: 90 + 36 = 126 36 + -12x + x2 = 126 Factor a perfect square on the left side: (x + -6)(x + -6) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + -6) equal to 11.22497216 and -11.22497216.Subproblem 1
x + -6 = 11.22497216 Simplifying x + -6 = 11.22497216 Reorder the terms: -6 + x = 11.22497216 Solving -6 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 11.22497216 + 6 Combine like terms: -6 + 6 = 0 0 + x = 11.22497216 + 6 x = 11.22497216 + 6 Combine like terms: 11.22497216 + 6 = 17.22497216 x = 17.22497216 Simplifying x = 17.22497216Subproblem 2
x + -6 = -11.22497216 Simplifying x + -6 = -11.22497216 Reorder the terms: -6 + x = -11.22497216 Solving -6 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -11.22497216 + 6 Combine like terms: -6 + 6 = 0 0 + x = -11.22497216 + 6 x = -11.22497216 + 6 Combine like terms: -11.22497216 + 6 = -5.22497216 x = -5.22497216 Simplifying x = -5.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.22497216, -5.22497216}Solution
x = {17.22497216, -5.22497216}
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