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Simplifying -2x2 + -14x + 144 = 0 Reorder the terms: 144 + -14x + -2x2 = 0 Solving 144 + -14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(72 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 72 + -7x + -1x2 = 0 Solving 72 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -72 + 7x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 7x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 7x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 7x + x2 = 0 + 72 7x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 7x + x2 = 72 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 72 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 72 + 12.25 Combine like terms: 72 + 12.25 = 84.25 12.25 + 7x + x2 = 84.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 3.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 3.5 = 9.178779875 Simplifying x + 3.5 = 9.178779875 Reorder the terms: 3.5 + x = 9.178779875 Solving 3.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.178779875 + -3.5 x = 9.178779875 + -3.5 Combine like terms: 9.178779875 + -3.5 = 5.678779875 x = 5.678779875 Simplifying x = 5.678779875Subproblem 2
x + 3.5 = -9.178779875 Simplifying x + 3.5 = -9.178779875 Reorder the terms: 3.5 + x = -9.178779875 Solving 3.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.178779875 + -3.5 x = -9.178779875 + -3.5 Combine like terms: -9.178779875 + -3.5 = -12.678779875 x = -12.678779875 Simplifying x = -12.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.678779875, -12.678779875}Solution
x = {5.678779875, -12.678779875}
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