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Simplifying -1x2 + 17x + -23 = 0 Reorder the terms: -23 + 17x + -1x2 = 0 Solving -23 + 17x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 23 + -17x + x2 = 0 Move the constant term to the right: Add '-23' to each side of the equation. 23 + -17x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -17x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -17x + x2 = 0 + -23 -17x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -17x + x2 = -23 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -23 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -23 + 72.25 Combine like terms: -23 + 72.25 = 49.25 72.25 + -17x + x2 = 49.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + -8.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + -8.5 = 7.017834424 Simplifying x + -8.5 = 7.017834424 Reorder the terms: -8.5 + x = 7.017834424 Solving -8.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.017834424 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.017834424 + 8.5 x = 7.017834424 + 8.5 Combine like terms: 7.017834424 + 8.5 = 15.517834424 x = 15.517834424 Simplifying x = 15.517834424Subproblem 2
x + -8.5 = -7.017834424 Simplifying x + -8.5 = -7.017834424 Reorder the terms: -8.5 + x = -7.017834424 Solving -8.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.017834424 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.017834424 + 8.5 x = -7.017834424 + 8.5 Combine like terms: -7.017834424 + 8.5 = 1.482165576 x = 1.482165576 Simplifying x = 1.482165576Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.517834424, 1.482165576}
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