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Simplifying 8x2 + 13x + 3 = 0 Reorder the terms: 3 + 13x + 8x2 = 0 Solving 3 + 13x + 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'. 0.375 + 1.625x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 1.625x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 1.625x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 1.625x + x2 = 0 + -0.375 1.625x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 1.625x + x2 = -0.375 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = -0.375 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = -0.375 + 0.66015625 Combine like terms: -0.375 + 0.66015625 = 0.28515625 0.66015625 + 1.625x + x2 = 0.28515625 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (x + 0.8125) equal to 0.534000234 and -0.534000234.Subproblem 1
x + 0.8125 = 0.534000234 Simplifying x + 0.8125 = 0.534000234 Reorder the terms: 0.8125 + x = 0.534000234 Solving 0.8125 + x = 0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 0.534000234 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 0.534000234 + -0.8125 x = 0.534000234 + -0.8125 Combine like terms: 0.534000234 + -0.8125 = -0.278499766 x = -0.278499766 Simplifying x = -0.278499766Subproblem 2
x + 0.8125 = -0.534000234 Simplifying x + 0.8125 = -0.534000234 Reorder the terms: 0.8125 + x = -0.534000234 Solving 0.8125 + x = -0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -0.534000234 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -0.534000234 + -0.8125 x = -0.534000234 + -0.8125 Combine like terms: -0.534000234 + -0.8125 = -1.346500234 x = -1.346500234 Simplifying x = -1.346500234Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.278499766, -1.346500234}
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