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Simplifying 8x2 + 52x + 58 = 0 Reorder the terms: 58 + 52x + 8x2 = 0 Solving 58 + 52x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 26x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 26x + 4x2)' equal to zero and attempt to solve: Simplifying 29 + 26x + 4x2 = 0 Solving 29 + 26x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.25 + 6.5x + x2 = 0 Move the constant term to the right: Add '-7.25' to each side of the equation. 7.25 + 6.5x + -7.25 + x2 = 0 + -7.25 Reorder the terms: 7.25 + -7.25 + 6.5x + x2 = 0 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + 6.5x + x2 = 0 + -7.25 6.5x + x2 = 0 + -7.25 Combine like terms: 0 + -7.25 = -7.25 6.5x + x2 = -7.25 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -7.25 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -7.25 + 10.5625 Combine like terms: -7.25 + 10.5625 = 3.3125 10.5625 + 6.5x + x2 = 3.3125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (x + 3.25) equal to 1.820027472 and -1.820027472.Subproblem 1
x + 3.25 = 1.820027472 Simplifying x + 3.25 = 1.820027472 Reorder the terms: 3.25 + x = 1.820027472 Solving 3.25 + x = 1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 1.820027472 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 1.820027472 + -3.25 x = 1.820027472 + -3.25 Combine like terms: 1.820027472 + -3.25 = -1.429972528 x = -1.429972528 Simplifying x = -1.429972528Subproblem 2
x + 3.25 = -1.820027472 Simplifying x + 3.25 = -1.820027472 Reorder the terms: 3.25 + x = -1.820027472 Solving 3.25 + x = -1.820027472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -1.820027472 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -1.820027472 + -3.25 x = -1.820027472 + -3.25 Combine like terms: -1.820027472 + -3.25 = -5.070027472 x = -5.070027472 Simplifying x = -5.070027472Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.429972528, -5.070027472}Solution
x = {-1.429972528, -5.070027472}
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