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Simplifying 2x2 + -62x + 240 = 0 Reorder the terms: 240 + -62x + 2x2 = 0 Solving 240 + -62x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(120 + -31x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(120 + -31x + x2)' equal to zero and attempt to solve: Simplifying 120 + -31x + x2 = 0 Solving 120 + -31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -31x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -31x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -31x + x2 = 0 + -120 -31x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -31x + x2 = -120 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -120 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -120 + 240.25 Combine like terms: -120 + 240.25 = 120.25 240.25 + -31x + x2 = 120.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -15.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -15.5 = 10.9658561 Simplifying x + -15.5 = 10.9658561 Reorder the terms: -15.5 + x = 10.9658561 Solving -15.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 10.9658561 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 10.9658561 + 15.5 x = 10.9658561 + 15.5 Combine like terms: 10.9658561 + 15.5 = 26.4658561 x = 26.4658561 Simplifying x = 26.4658561Subproblem 2
x + -15.5 = -10.9658561 Simplifying x + -15.5 = -10.9658561 Reorder the terms: -15.5 + x = -10.9658561 Solving -15.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -10.9658561 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -10.9658561 + 15.5 x = -10.9658561 + 15.5 Combine like terms: -10.9658561 + 15.5 = 4.5341439 x = 4.5341439 Simplifying x = 4.5341439Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.4658561, 4.5341439}Solution
x = {26.4658561, 4.5341439}
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