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Simplifying 0 = x2 + -17x + 50 Reorder the terms: 0 = 50 + -17x + x2 Solving 0 = 50 + -17x + x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 17x + -1x2 = 50 + -17x + x2 + -50 + 17x + -1x2 Reorder the terms: -50 + 17x + -1x2 = 50 + -50 + -17x + 17x + x2 + -1x2 Combine like terms: 50 + -50 = 0 -50 + 17x + -1x2 = 0 + -17x + 17x + x2 + -1x2 -50 + 17x + -1x2 = -17x + 17x + x2 + -1x2 Combine like terms: -17x + 17x = 0 -50 + 17x + -1x2 = 0 + x2 + -1x2 -50 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -17x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -17x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -17x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -17x + x2 = 0 + -50 -17x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -17x + x2 = -50 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 = -50 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -50 + 72.25 Combine like terms: -50 + 72.25 = 22.25 72.25 + -17x + x2 = 22.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -8.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -8.5 = 4.716990566 Simplifying x + -8.5 = 4.716990566 Reorder the terms: -8.5 + x = 4.716990566 Solving -8.5 + x = 4.716990566 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 = 4.716990566 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.716990566 + 8.5 x = 4.716990566 + 8.5 Combine like terms: 4.716990566 + 8.5 = 13.216990566 x = 13.216990566 Simplifying x = 13.216990566Subproblem 2
x + -8.5 = -4.716990566 Simplifying x + -8.5 = -4.716990566 Reorder the terms: -8.5 + x = -4.716990566 Solving -8.5 + x = -4.716990566 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 = -4.716990566 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.716990566 + 8.5 x = -4.716990566 + 8.5 Combine like terms: -4.716990566 + 8.5 = 3.783009434 x = 3.783009434 Simplifying x = 3.783009434Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.216990566, 3.783009434}
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