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Simplifying x2 + -17x + 15 = 0 Reorder the terms: 15 + -17x + x2 = 0 Solving 15 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -17x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -17x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -17x + x2 = 0 + -15 -17x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -17x + x2 = -15 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 = -15 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -15 + 72.25 Combine like terms: -15 + 72.25 = 57.25 72.25 + -17x + x2 = 57.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -8.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -8.5 = 7.566372975 Simplifying x + -8.5 = 7.566372975 Reorder the terms: -8.5 + x = 7.566372975 Solving -8.5 + x = 7.566372975 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 = 7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.566372975 + 8.5 x = 7.566372975 + 8.5 Combine like terms: 7.566372975 + 8.5 = 16.066372975 x = 16.066372975 Simplifying x = 16.066372975Subproblem 2
x + -8.5 = -7.566372975 Simplifying x + -8.5 = -7.566372975 Reorder the terms: -8.5 + x = -7.566372975 Solving -8.5 + x = -7.566372975 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 = -7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.566372975 + 8.5 x = -7.566372975 + 8.5 Combine like terms: -7.566372975 + 8.5 = 0.933627025 x = 0.933627025 Simplifying x = 0.933627025Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.066372975, 0.933627025}
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