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Simplifying 8x2 + -20x + -9 = 0 Reorder the terms: -9 + -20x + 8x2 = 0 Solving -9 + -20x + 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'. -1.125 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -2.5x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -2.5x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -2.5x + x2 = 0 + 1.125 -2.5x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -2.5x + x2 = 1.125 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.125 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.125 + 1.5625 Combine like terms: 1.125 + 1.5625 = 2.6875 1.5625 + -2.5x + x2 = 2.6875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.6875 Calculate the square root of the right side: 1.639359631 Break this problem into two subproblems by setting (x + -1.25) equal to 1.639359631 and -1.639359631.Subproblem 1
x + -1.25 = 1.639359631 Simplifying x + -1.25 = 1.639359631 Reorder the terms: -1.25 + x = 1.639359631 Solving -1.25 + x = 1.639359631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.639359631 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.639359631 + 1.25 x = 1.639359631 + 1.25 Combine like terms: 1.639359631 + 1.25 = 2.889359631 x = 2.889359631 Simplifying x = 2.889359631Subproblem 2
x + -1.25 = -1.639359631 Simplifying x + -1.25 = -1.639359631 Reorder the terms: -1.25 + x = -1.639359631 Solving -1.25 + x = -1.639359631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.639359631 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.639359631 + 1.25 x = -1.639359631 + 1.25 Combine like terms: -1.639359631 + 1.25 = -0.389359631 x = -0.389359631 Simplifying x = -0.389359631Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.889359631, -0.389359631}
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