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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 = 4.03515625 3.28515625 + 3.625x + x2 = 4.03515625 Factor a perfect square on the left side: (x + 1.8125)(x + 1.8125) = 4.03515625 Calculate the square root of the right side: 2.008769835 Break this problem into two subproblems by setting (x + 1.8125) equal to 2.008769835 and -2.008769835.Subproblem 1
x + 1.8125 = 2.008769835 Simplifying x + 1.8125 = 2.008769835 Reorder the terms: 1.8125 + x = 2.008769835 Solving 1.8125 + x = 2.008769835 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 = 2.008769835 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = 2.008769835 + -1.8125 x = 2.008769835 + -1.8125 Combine like terms: 2.008769835 + -1.8125 = 0.196269835 x = 0.196269835 Simplifying x = 0.196269835Subproblem 2
x + 1.8125 = -2.008769835 Simplifying x + 1.8125 = -2.008769835 Reorder the terms: 1.8125 + x = -2.008769835 Solving 1.8125 + x = -2.008769835 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 = -2.008769835 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = -2.008769835 + -1.8125 x = -2.008769835 + -1.8125 Combine like terms: -2.008769835 + -1.8125 = -3.821269835 x = -3.821269835 Simplifying x = -3.821269835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196269835, -3.821269835}
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