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Simplifying 4x2 + 58x + -272 = 0 Reorder the terms: -272 + 58x + 4x2 = 0 Solving -272 + 58x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-136 + 29x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-136 + 29x + 2x2)' equal to zero and attempt to solve: Simplifying -136 + 29x + 2x2 = 0 Solving -136 + 29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -68 + 14.5x + x2 = 0 Move the constant term to the right: Add '68' to each side of the equation. -68 + 14.5x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 14.5x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 14.5x + x2 = 0 + 68 14.5x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 14.5x + x2 = 68 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 68 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 68 + 52.5625 Combine like terms: 68 + 52.5625 = 120.5625 52.5625 + 14.5x + x2 = 120.5625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 120.5625 Calculate the square root of the right side: 10.980095628 Break this problem into two subproblems by setting (x + 7.25) equal to 10.980095628 and -10.980095628.Subproblem 1
x + 7.25 = 10.980095628 Simplifying x + 7.25 = 10.980095628 Reorder the terms: 7.25 + x = 10.980095628 Solving 7.25 + x = 10.980095628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 10.980095628 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 10.980095628 + -7.25 x = 10.980095628 + -7.25 Combine like terms: 10.980095628 + -7.25 = 3.730095628 x = 3.730095628 Simplifying x = 3.730095628Subproblem 2
x + 7.25 = -10.980095628 Simplifying x + 7.25 = -10.980095628 Reorder the terms: 7.25 + x = -10.980095628 Solving 7.25 + x = -10.980095628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -10.980095628 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -10.980095628 + -7.25 x = -10.980095628 + -7.25 Combine like terms: -10.980095628 + -7.25 = -18.230095628 x = -18.230095628 Simplifying x = -18.230095628Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.730095628, -18.230095628}Solution
x = {3.730095628, -18.230095628}
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