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Simplifying 8x2 + 52x + 30 = 0 Reorder the terms: 30 + 52x + 8x2 = 0 Solving 30 + 52x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 26x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 26x + 4x2)' equal to zero and attempt to solve: Simplifying 15 + 26x + 4x2 = 0 Solving 15 + 26x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 6.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 6.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 6.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 6.5x + x2 = 0 + -3.75 6.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 6.5x + x2 = -3.75 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 = -3.75 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -3.75 + 10.5625 Combine like terms: -3.75 + 10.5625 = 6.8125 10.5625 + 6.5x + x2 = 6.8125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (x + 3.25) equal to 2.610076627 and -2.610076627.Subproblem 1
x + 3.25 = 2.610076627 Simplifying x + 3.25 = 2.610076627 Reorder the terms: 3.25 + x = 2.610076627 Solving 3.25 + x = 2.610076627 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 = 2.610076627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.610076627 + -3.25 x = 2.610076627 + -3.25 Combine like terms: 2.610076627 + -3.25 = -0.639923373 x = -0.639923373 Simplifying x = -0.639923373Subproblem 2
x + 3.25 = -2.610076627 Simplifying x + 3.25 = -2.610076627 Reorder the terms: 3.25 + x = -2.610076627 Solving 3.25 + x = -2.610076627 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 = -2.610076627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.610076627 + -3.25 x = -2.610076627 + -3.25 Combine like terms: -2.610076627 + -3.25 = -5.860076627 x = -5.860076627 Simplifying x = -5.860076627Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.639923373, -5.860076627}Solution
x = {-0.639923373, -5.860076627}
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