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Simplifying 8x2 + 17x + 6 = 0 Reorder the terms: 6 + 17x + 8x2 = 0 Solving 6 + 17x + 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 + 2.125x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2.125x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2.125x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2.125x + x2 = 0 + -0.75 2.125x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2.125x + x2 = -0.75 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = -0.75 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = -0.75 + 1.12890625 Combine like terms: -0.75 + 1.12890625 = 0.37890625 1.12890625 + 2.125x + x2 = 0.37890625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + 1.0625) equal to 0.615553613 and -0.615553613.Subproblem 1
x + 1.0625 = 0.615553613 Simplifying x + 1.0625 = 0.615553613 Reorder the terms: 1.0625 + x = 0.615553613 Solving 1.0625 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 0.615553613 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 0.615553613 + -1.0625 x = 0.615553613 + -1.0625 Combine like terms: 0.615553613 + -1.0625 = -0.446946387 x = -0.446946387 Simplifying x = -0.446946387Subproblem 2
x + 1.0625 = -0.615553613 Simplifying x + 1.0625 = -0.615553613 Reorder the terms: 1.0625 + x = -0.615553613 Solving 1.0625 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -0.615553613 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -0.615553613 + -1.0625 x = -0.615553613 + -1.0625 Combine like terms: -0.615553613 + -1.0625 = -1.678053613 x = -1.678053613 Simplifying x = -1.678053613Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.446946387, -1.678053613}
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