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Simplifying 17x + -1x2 = -52 Solving 17x + -1x2 = -52 Solving for variable 'x'. Reorder the terms: 52 + 17x + -1x2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + -17x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -17x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -17x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -17x + x2 = 0 + 52 -17x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -17x + x2 = 52 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 = 52 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 52 + 72.25 Combine like terms: 52 + 72.25 = 124.25 72.25 + -17x + x2 = 124.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + -8.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + -8.5 = 11.146748405 Simplifying x + -8.5 = 11.146748405 Reorder the terms: -8.5 + x = 11.146748405 Solving -8.5 + x = 11.146748405 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 = 11.146748405 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 11.146748405 + 8.5 x = 11.146748405 + 8.5 Combine like terms: 11.146748405 + 8.5 = 19.646748405 x = 19.646748405 Simplifying x = 19.646748405Subproblem 2
x + -8.5 = -11.146748405 Simplifying x + -8.5 = -11.146748405 Reorder the terms: -8.5 + x = -11.146748405 Solving -8.5 + x = -11.146748405 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 = -11.146748405 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -11.146748405 + 8.5 x = -11.146748405 + 8.5 Combine like terms: -11.146748405 + 8.5 = -2.646748405 x = -2.646748405 Simplifying x = -2.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.646748405, -2.646748405}
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