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Simplifying 8x2 + 29x + 6 = 0 Reorder the terms: 6 + 29x + 8x2 = 0 Solving 6 + 29x + 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'. 0.75 + 3.625x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 3.625x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 3.625x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 3.625x + x2 = 0 + -0.75 3.625x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 3.625x + x2 = -0.75 The x term is 3.625x. Take half its coefficient (1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. 3.625x + 3.28515625 + x2 = -0.75 + 3.28515625 Reorder the terms: 3.28515625 + 3.625x + x2 = -0.75 + 3.28515625 Combine like terms: -0.75 + 3.28515625 = 2.53515625 3.28515625 + 3.625x + x2 = 2.53515625 Factor a perfect square on the left side: (x + 1.8125)(x + 1.8125) = 2.53515625 Calculate the square root of the right side: 1.5922174 Break this problem into two subproblems by setting (x + 1.8125) equal to 1.5922174 and -1.5922174.Subproblem 1
x + 1.8125 = 1.5922174 Simplifying x + 1.8125 = 1.5922174 Reorder the terms: 1.8125 + x = 1.5922174 Solving 1.8125 + x = 1.5922174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + x = 1.5922174 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = 1.5922174 + -1.8125 x = 1.5922174 + -1.8125 Combine like terms: 1.5922174 + -1.8125 = -0.2202826 x = -0.2202826 Simplifying x = -0.2202826Subproblem 2
x + 1.8125 = -1.5922174 Simplifying x + 1.8125 = -1.5922174 Reorder the terms: 1.8125 + x = -1.5922174 Solving 1.8125 + x = -1.5922174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + x = -1.5922174 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = -1.5922174 + -1.8125 x = -1.5922174 + -1.8125 Combine like terms: -1.5922174 + -1.8125 = -3.4047174 x = -3.4047174 Simplifying x = -3.4047174Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2202826, -3.4047174}
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