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Simplifying x2 + -17x + 65 = 0 Reorder the terms: 65 + -17x + x2 = 0 Solving 65 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-65' to each side of the equation. 65 + -17x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + -17x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -17x + x2 = 0 + -65 -17x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 -17x + x2 = -65 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 = -65 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -65 + 72.25 Combine like terms: -65 + 72.25 = 7.25 72.25 + -17x + x2 = 7.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -8.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -8.5 = 2.692582404 Simplifying x + -8.5 = 2.692582404 Reorder the terms: -8.5 + x = 2.692582404 Solving -8.5 + x = 2.692582404 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 = 2.692582404 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 2.692582404 + 8.5 x = 2.692582404 + 8.5 Combine like terms: 2.692582404 + 8.5 = 11.192582404 x = 11.192582404 Simplifying x = 11.192582404Subproblem 2
x + -8.5 = -2.692582404 Simplifying x + -8.5 = -2.692582404 Reorder the terms: -8.5 + x = -2.692582404 Solving -8.5 + x = -2.692582404 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 = -2.692582404 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -2.692582404 + 8.5 x = -2.692582404 + 8.5 Combine like terms: -2.692582404 + 8.5 = 5.807417596 x = 5.807417596 Simplifying x = 5.807417596Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.192582404, 5.807417596}
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