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Simplifying 0 = 2x2 + -74x + 448 Reorder the terms: 0 = 448 + -74x + 2x2 Solving 0 = 448 + -74x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -448 = -448 -448 + 74x + -2x2 = 448 + -74x + 2x2 + -448 + 74x + -2x2 Reorder the terms: -448 + 74x + -2x2 = 448 + -448 + -74x + 74x + 2x2 + -2x2 Combine like terms: 448 + -448 = 0 -448 + 74x + -2x2 = 0 + -74x + 74x + 2x2 + -2x2 -448 + 74x + -2x2 = -74x + 74x + 2x2 + -2x2 Combine like terms: -74x + 74x = 0 -448 + 74x + -2x2 = 0 + 2x2 + -2x2 -448 + 74x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -448 + 74x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-224 + 37x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-224 + 37x + -1x2)' equal to zero and attempt to solve: Simplifying -224 + 37x + -1x2 = 0 Solving -224 + 37x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 224 + -37x + x2 = 0 Move the constant term to the right: Add '-224' to each side of the equation. 224 + -37x + -224 + x2 = 0 + -224 Reorder the terms: 224 + -224 + -37x + x2 = 0 + -224 Combine like terms: 224 + -224 = 0 0 + -37x + x2 = 0 + -224 -37x + x2 = 0 + -224 Combine like terms: 0 + -224 = -224 -37x + x2 = -224 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -224 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -224 + 342.25 Combine like terms: -224 + 342.25 = 118.25 342.25 + -37x + x2 = 118.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + -18.5) equal to 10.874281585 and -10.874281585.Subproblem 1
x + -18.5 = 10.874281585 Simplifying x + -18.5 = 10.874281585 Reorder the terms: -18.5 + x = 10.874281585 Solving -18.5 + x = 10.874281585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 10.874281585 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 10.874281585 + 18.5 x = 10.874281585 + 18.5 Combine like terms: 10.874281585 + 18.5 = 29.374281585 x = 29.374281585 Simplifying x = 29.374281585Subproblem 2
x + -18.5 = -10.874281585 Simplifying x + -18.5 = -10.874281585 Reorder the terms: -18.5 + x = -10.874281585 Solving -18.5 + x = -10.874281585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -10.874281585 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -10.874281585 + 18.5 x = -10.874281585 + 18.5 Combine like terms: -10.874281585 + 18.5 = 7.625718415 x = 7.625718415 Simplifying x = 7.625718415Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.374281585, 7.625718415}Solution
x = {29.374281585, 7.625718415}
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