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Simplifying 8x2 + 41x + -39 = 0 Reorder the terms: -39 + 41x + 8x2 = 0 Solving -39 + 41x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.875 + 5.125x + x2 = 0 Move the constant term to the right: Add '4.875' to each side of the equation. -4.875 + 5.125x + 4.875 + x2 = 0 + 4.875 Reorder the terms: -4.875 + 4.875 + 5.125x + x2 = 0 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + 5.125x + x2 = 0 + 4.875 5.125x + x2 = 0 + 4.875 Combine like terms: 0 + 4.875 = 4.875 5.125x + x2 = 4.875 The x term is 5.125x. Take half its coefficient (2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. 5.125x + 6.56640625 + x2 = 4.875 + 6.56640625 Reorder the terms: 6.56640625 + 5.125x + x2 = 4.875 + 6.56640625 Combine like terms: 4.875 + 6.56640625 = 11.44140625 6.56640625 + 5.125x + x2 = 11.44140625 Factor a perfect square on the left side: (x + 2.5625)(x + 2.5625) = 11.44140625 Calculate the square root of the right side: 3.382514782 Break this problem into two subproblems by setting (x + 2.5625) equal to 3.382514782 and -3.382514782.Subproblem 1
x + 2.5625 = 3.382514782 Simplifying x + 2.5625 = 3.382514782 Reorder the terms: 2.5625 + x = 3.382514782 Solving 2.5625 + x = 3.382514782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = 3.382514782 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = 3.382514782 + -2.5625 x = 3.382514782 + -2.5625 Combine like terms: 3.382514782 + -2.5625 = 0.820014782 x = 0.820014782 Simplifying x = 0.820014782Subproblem 2
x + 2.5625 = -3.382514782 Simplifying x + 2.5625 = -3.382514782 Reorder the terms: 2.5625 + x = -3.382514782 Solving 2.5625 + x = -3.382514782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5625' to each side of the equation. 2.5625 + -2.5625 + x = -3.382514782 + -2.5625 Combine like terms: 2.5625 + -2.5625 = 0.0000 0.0000 + x = -3.382514782 + -2.5625 x = -3.382514782 + -2.5625 Combine like terms: -3.382514782 + -2.5625 = -5.945014782 x = -5.945014782 Simplifying x = -5.945014782Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.820014782, -5.945014782}
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