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Simplifying 8x2 + 57x + 13 = 0 Reorder the terms: 13 + 57x + 8x2 = 0 Solving 13 + 57x + 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'. 1.625 + 7.125x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + 7.125x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + 7.125x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + 7.125x + x2 = 0 + -1.625 7.125x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 7.125x + x2 = -1.625 The x term is 7.125x. Take half its coefficient (3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. 7.125x + 12.69140625 + x2 = -1.625 + 12.69140625 Reorder the terms: 12.69140625 + 7.125x + x2 = -1.625 + 12.69140625 Combine like terms: -1.625 + 12.69140625 = 11.06640625 12.69140625 + 7.125x + x2 = 11.06640625 Factor a perfect square on the left side: (x + 3.5625)(x + 3.5625) = 11.06640625 Calculate the square root of the right side: 3.326620846 Break this problem into two subproblems by setting (x + 3.5625) equal to 3.326620846 and -3.326620846.Subproblem 1
x + 3.5625 = 3.326620846 Simplifying x + 3.5625 = 3.326620846 Reorder the terms: 3.5625 + x = 3.326620846 Solving 3.5625 + x = 3.326620846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5625' to each side of the equation. 3.5625 + -3.5625 + x = 3.326620846 + -3.5625 Combine like terms: 3.5625 + -3.5625 = 0.0000 0.0000 + x = 3.326620846 + -3.5625 x = 3.326620846 + -3.5625 Combine like terms: 3.326620846 + -3.5625 = -0.235879154 x = -0.235879154 Simplifying x = -0.235879154Subproblem 2
x + 3.5625 = -3.326620846 Simplifying x + 3.5625 = -3.326620846 Reorder the terms: 3.5625 + x = -3.326620846 Solving 3.5625 + x = -3.326620846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5625' to each side of the equation. 3.5625 + -3.5625 + x = -3.326620846 + -3.5625 Combine like terms: 3.5625 + -3.5625 = 0.0000 0.0000 + x = -3.326620846 + -3.5625 x = -3.326620846 + -3.5625 Combine like terms: -3.326620846 + -3.5625 = -6.889120846 x = -6.889120846 Simplifying x = -6.889120846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.235879154, -6.889120846}
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