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Simplifying 2x2 + -40x + 144 = 0 Reorder the terms: 144 + -40x + 2x2 = 0 Solving 144 + -40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(72 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + -20x + x2)' equal to zero and attempt to solve: Simplifying 72 + -20x + x2 = 0 Solving 72 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -20x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -20x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -20x + x2 = 0 + -72 -20x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -20x + x2 = -72 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -72 + 100 Reorder the terms: 100 + -20x + x2 = -72 + 100 Combine like terms: -72 + 100 = 28 100 + -20x + x2 = 28 Factor a perfect square on the left side: (x + -10)(x + -10) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -10) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -10 = 5.291502622 Simplifying x + -10 = 5.291502622 Reorder the terms: -10 + x = 5.291502622 Solving -10 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.291502622 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.291502622 + 10 x = 5.291502622 + 10 Combine like terms: 5.291502622 + 10 = 15.291502622 x = 15.291502622 Simplifying x = 15.291502622Subproblem 2
x + -10 = -5.291502622 Simplifying x + -10 = -5.291502622 Reorder the terms: -10 + x = -5.291502622 Solving -10 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.291502622 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.291502622 + 10 x = -5.291502622 + 10 Combine like terms: -5.291502622 + 10 = 4.708497378 x = 4.708497378 Simplifying x = 4.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.291502622, 4.708497378}Solution
x = {15.291502622, 4.708497378}
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