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Simplifying 0 = 2x2 + 56x + -204 Reorder the terms: 0 = -204 + 56x + 2x2 Solving 0 = -204 + 56x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 204 = 204 204 + -56x + -2x2 = -204 + 56x + 2x2 + 204 + -56x + -2x2 Reorder the terms: 204 + -56x + -2x2 = -204 + 204 + 56x + -56x + 2x2 + -2x2 Combine like terms: -204 + 204 = 0 204 + -56x + -2x2 = 0 + 56x + -56x + 2x2 + -2x2 204 + -56x + -2x2 = 56x + -56x + 2x2 + -2x2 Combine like terms: 56x + -56x = 0 204 + -56x + -2x2 = 0 + 2x2 + -2x2 204 + -56x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 204 + -56x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(102 + -28x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(102 + -28x + -1x2)' equal to zero and attempt to solve: Simplifying 102 + -28x + -1x2 = 0 Solving 102 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -102 + 28x + x2 = 0 Move the constant term to the right: Add '102' to each side of the equation. -102 + 28x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 28x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 28x + x2 = 0 + 102 28x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 28x + x2 = 102 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 102 + 196 Reorder the terms: 196 + 28x + x2 = 102 + 196 Combine like terms: 102 + 196 = 298 196 + 28x + x2 = 298 Factor a perfect square on the left side: (x + 14)(x + 14) = 298 Calculate the square root of the right side: 17.262676502 Break this problem into two subproblems by setting (x + 14) equal to 17.262676502 and -17.262676502.Subproblem 1
x + 14 = 17.262676502 Simplifying x + 14 = 17.262676502 Reorder the terms: 14 + x = 17.262676502 Solving 14 + x = 17.262676502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 17.262676502 + -14 Combine like terms: 14 + -14 = 0 0 + x = 17.262676502 + -14 x = 17.262676502 + -14 Combine like terms: 17.262676502 + -14 = 3.262676502 x = 3.262676502 Simplifying x = 3.262676502Subproblem 2
x + 14 = -17.262676502 Simplifying x + 14 = -17.262676502 Reorder the terms: 14 + x = -17.262676502 Solving 14 + x = -17.262676502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -17.262676502 + -14 Combine like terms: 14 + -14 = 0 0 + x = -17.262676502 + -14 x = -17.262676502 + -14 Combine like terms: -17.262676502 + -14 = -31.262676502 x = -31.262676502 Simplifying x = -31.262676502Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.262676502, -31.262676502}Solution
x = {3.262676502, -31.262676502}
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