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Simplifying 5x2 + -60x + 40 = 0 Reorder the terms: 40 + -60x + 5x2 = 0 Solving 40 + -60x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + -12x + x2)' equal to zero and attempt to solve: Simplifying 8 + -12x + x2 = 0 Solving 8 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -12x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -12x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -12x + x2 = 0 + -8 -12x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -12x + x2 = -8 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 = -8 + 36 Reorder the terms: 36 + -12x + x2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + -12x + x2 = 28 Factor a perfect square on the left side: (x + -6)(x + -6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -6) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -6 = 5.291502622 Simplifying x + -6 = 5.291502622 Reorder the terms: -6 + x = 5.291502622 Solving -6 + x = 5.291502622 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 = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.291502622 + 6 x = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 x = 11.291502622 Simplifying x = 11.291502622Subproblem 2
x + -6 = -5.291502622 Simplifying x + -6 = -5.291502622 Reorder the terms: -6 + x = -5.291502622 Solving -6 + x = -5.291502622 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 = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.291502622 + 6 x = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 x = 0.708497378 Simplifying x = 0.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.291502622, 0.708497378}Solution
x = {11.291502622, 0.708497378}
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