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Simplifying x2 + -17x + -66 = 0 Reorder the terms: -66 + -17x + x2 = 0 Solving -66 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -17x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + -17x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -17x + x2 = 0 + 66 -17x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 -17x + x2 = 66 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 = 66 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 66 + 72.25 Combine like terms: 66 + 72.25 = 138.25 72.25 + -17x + x2 = 138.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + -8.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + -8.5 = 11.757976016 Simplifying x + -8.5 = 11.757976016 Reorder the terms: -8.5 + x = 11.757976016 Solving -8.5 + x = 11.757976016 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 = 11.757976016 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 11.757976016 + 8.5 x = 11.757976016 + 8.5 Combine like terms: 11.757976016 + 8.5 = 20.257976016 x = 20.257976016 Simplifying x = 20.257976016Subproblem 2
x + -8.5 = -11.757976016 Simplifying x + -8.5 = -11.757976016 Reorder the terms: -8.5 + x = -11.757976016 Solving -8.5 + x = -11.757976016 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 = -11.757976016 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -11.757976016 + 8.5 x = -11.757976016 + 8.5 Combine like terms: -11.757976016 + 8.5 = -3.257976016 x = -3.257976016 Simplifying x = -3.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.257976016, -3.257976016}
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