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Simplifying 8x2 + 9x + 2 = 0 Reorder the terms: 2 + 9x + 8x2 = 0 Solving 2 + 9x + 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'. 0.25 + 1.125x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.125x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.125x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.125x + x2 = 0 + -0.25 1.125x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.125x + x2 = -0.25 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = -0.25 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = -0.25 + 0.31640625 Combine like terms: -0.25 + 0.31640625 = 0.06640625 0.31640625 + 1.125x + x2 = 0.06640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.257694102 and -0.257694102.Subproblem 1
x + 0.5625 = 0.257694102 Simplifying x + 0.5625 = 0.257694102 Reorder the terms: 0.5625 + x = 0.257694102 Solving 0.5625 + x = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.257694102 + -0.5625 x = 0.257694102 + -0.5625 Combine like terms: 0.257694102 + -0.5625 = -0.304805898 x = -0.304805898 Simplifying x = -0.304805898Subproblem 2
x + 0.5625 = -0.257694102 Simplifying x + 0.5625 = -0.257694102 Reorder the terms: 0.5625 + x = -0.257694102 Solving 0.5625 + x = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.257694102 + -0.5625 x = -0.257694102 + -0.5625 Combine like terms: -0.257694102 + -0.5625 = -0.820194102 x = -0.820194102 Simplifying x = -0.820194102Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.304805898, -0.820194102}
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