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Simplifying x(2x + -1) = 17 Reorder the terms: x(-1 + 2x) = 17 (-1 * x + 2x * x) = 17 (-1x + 2x2) = 17 Solving -1x + 2x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -1x + 2x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -0.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -0.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -0.5x + x2 = 0 + 8.5 -0.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -0.5x + x2 = 8.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 8.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 8.5 + 0.0625 Combine like terms: 8.5 + 0.0625 = 8.5625 0.0625 + -0.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + -0.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + -0.25 = 2.926174978 Simplifying x + -0.25 = 2.926174978 Reorder the terms: -0.25 + x = 2.926174978 Solving -0.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.926174978 + 0.25 x = 2.926174978 + 0.25 Combine like terms: 2.926174978 + 0.25 = 3.176174978 x = 3.176174978 Simplifying x = 3.176174978Subproblem 2
x + -0.25 = -2.926174978 Simplifying x + -0.25 = -2.926174978 Reorder the terms: -0.25 + x = -2.926174978 Solving -0.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.926174978 + 0.25 x = -2.926174978 + 0.25 Combine like terms: -2.926174978 + 0.25 = -2.676174978 x = -2.676174978 Simplifying x = -2.676174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.176174978, -2.676174978}
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