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Simplifying 240 = 2x2 + 2x Reorder the terms: 240 = 2x + 2x2 Solving 240 = 2x + 2x2 Solving for variable 'x'. Reorder the terms: 240 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 240 + -2x + -2x2 = 0 + 2x2 + -2x2 240 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 240 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(120 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(120 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 120 + -1x + -1x2 = 0 Solving 120 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + x + x2 = 0 + 120 x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 x + x2 = 120 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 120 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 120 + 0.25 Combine like terms: 120 + 0.25 = 120.25 1.25 + x2 = 120.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 0.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 0.5 = 10.9658561 Simplifying x + 0.5 = 10.9658561 Reorder the terms: 0.5 + x = 10.9658561 Solving 0.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.9658561 + -0.5 x = 10.9658561 + -0.5 Combine like terms: 10.9658561 + -0.5 = 10.4658561 x = 10.4658561 Simplifying x = 10.4658561Subproblem 2
x + 0.5 = -10.9658561 Simplifying x + 0.5 = -10.9658561 Reorder the terms: 0.5 + x = -10.9658561 Solving 0.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.9658561 + -0.5 x = -10.9658561 + -0.5 Combine like terms: -10.9658561 + -0.5 = -11.4658561 x = -11.4658561 Simplifying x = -11.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.4658561, -11.4658561}Solution
x = {10.4658561, -11.4658561}
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