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Simplifying 10 = x2 + -17x Reorder the terms: 10 = -17x + x2 Solving 10 = -17x + x2 Solving for variable 'x'. Reorder the terms: 10 + 17x + -1x2 = -17x + 17x + x2 + -1x2 Combine like terms: -17x + 17x = 0 10 + 17x + -1x2 = 0 + x2 + -1x2 10 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -17x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -17x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -17x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -17x + x2 = 0 + 10 -17x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -17x + x2 = 10 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 = 10 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 10 + 72.25 Combine like terms: 10 + 72.25 = 82.25 72.25 + -17x + x2 = 82.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -8.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -8.5 = 9.069178574 Simplifying x + -8.5 = 9.069178574 Reorder the terms: -8.5 + x = 9.069178574 Solving -8.5 + x = 9.069178574 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 = 9.069178574 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.069178574 + 8.5 x = 9.069178574 + 8.5 Combine like terms: 9.069178574 + 8.5 = 17.569178574 x = 17.569178574 Simplifying x = 17.569178574Subproblem 2
x + -8.5 = -9.069178574 Simplifying x + -8.5 = -9.069178574 Reorder the terms: -8.5 + x = -9.069178574 Solving -8.5 + x = -9.069178574 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 = -9.069178574 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.069178574 + 8.5 x = -9.069178574 + 8.5 Combine like terms: -9.069178574 + 8.5 = -0.569178574 x = -0.569178574 Simplifying x = -0.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.569178574, -0.569178574}
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