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Simplifying 88 = x2 + -17x + 66 Reorder the terms: 88 = 66 + -17x + x2 Solving 88 = 66 + -17x + x2 Solving for variable 'x'. Combine like terms: 88 + -66 = 22 22 + 17x + -1x2 = 66 + -17x + x2 + -66 + 17x + -1x2 Reorder the terms: 22 + 17x + -1x2 = 66 + -66 + -17x + 17x + x2 + -1x2 Combine like terms: 66 + -66 = 0 22 + 17x + -1x2 = 0 + -17x + 17x + x2 + -1x2 22 + 17x + -1x2 = -17x + 17x + x2 + -1x2 Combine like terms: -17x + 17x = 0 22 + 17x + -1x2 = 0 + x2 + -1x2 22 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + -17x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -17x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -17x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -17x + x2 = 0 + 22 -17x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -17x + x2 = 22 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 = 22 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 22 + 72.25 Combine like terms: 22 + 72.25 = 94.25 72.25 + -17x + x2 = 94.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + -8.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + -8.5 = 9.708243919 Simplifying x + -8.5 = 9.708243919 Reorder the terms: -8.5 + x = 9.708243919 Solving -8.5 + x = 9.708243919 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 = 9.708243919 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.708243919 + 8.5 x = 9.708243919 + 8.5 Combine like terms: 9.708243919 + 8.5 = 18.208243919 x = 18.208243919 Simplifying x = 18.208243919Subproblem 2
x + -8.5 = -9.708243919 Simplifying x + -8.5 = -9.708243919 Reorder the terms: -8.5 + x = -9.708243919 Solving -8.5 + x = -9.708243919 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 = -9.708243919 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.708243919 + 8.5 x = -9.708243919 + 8.5 Combine like terms: -9.708243919 + 8.5 = -1.208243919 x = -1.208243919 Simplifying x = -1.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.208243919, -1.208243919}
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