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Simplifying 2x2 + -90x + 540 = 0 Reorder the terms: 540 + -90x + 2x2 = 0 Solving 540 + -90x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(270 + -45x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(270 + -45x + x2)' equal to zero and attempt to solve: Simplifying 270 + -45x + x2 = 0 Solving 270 + -45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-270' to each side of the equation. 270 + -45x + -270 + x2 = 0 + -270 Reorder the terms: 270 + -270 + -45x + x2 = 0 + -270 Combine like terms: 270 + -270 = 0 0 + -45x + x2 = 0 + -270 -45x + x2 = 0 + -270 Combine like terms: 0 + -270 = -270 -45x + x2 = -270 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = -270 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -270 + 506.25 Combine like terms: -270 + 506.25 = 236.25 506.25 + -45x + x2 = 236.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + -22.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + -22.5 = 15.370426149 Simplifying x + -22.5 = 15.370426149 Reorder the terms: -22.5 + x = 15.370426149 Solving -22.5 + x = 15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 15.370426149 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 15.370426149 + 22.5 x = 15.370426149 + 22.5 Combine like terms: 15.370426149 + 22.5 = 37.870426149 x = 37.870426149 Simplifying x = 37.870426149Subproblem 2
x + -22.5 = -15.370426149 Simplifying x + -22.5 = -15.370426149 Reorder the terms: -22.5 + x = -15.370426149 Solving -22.5 + x = -15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -15.370426149 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -15.370426149 + 22.5 x = -15.370426149 + 22.5 Combine like terms: -15.370426149 + 22.5 = 7.129573851 x = 7.129573851 Simplifying x = 7.129573851Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.870426149, 7.129573851}Solution
x = {37.870426149, 7.129573851}
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