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Simplifying (x2 + 17x + -64) = 0 Reorder the terms: (-64 + 17x + x2) = 0 Remove parenthesis around (-64 + 17x + x2) -64 + 17x + x2 = 0 Solving -64 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 17x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 17x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 17x + x2 = 0 + 64 17x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 17x + x2 = 64 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 = 64 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 64 + 72.25 Combine like terms: 64 + 72.25 = 136.25 72.25 + 17x + x2 = 136.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + 8.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + 8.5 = 11.67261753 Simplifying x + 8.5 = 11.67261753 Reorder the terms: 8.5 + x = 11.67261753 Solving 8.5 + x = 11.67261753 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 = 11.67261753 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.67261753 + -8.5 x = 11.67261753 + -8.5 Combine like terms: 11.67261753 + -8.5 = 3.17261753 x = 3.17261753 Simplifying x = 3.17261753Subproblem 2
x + 8.5 = -11.67261753 Simplifying x + 8.5 = -11.67261753 Reorder the terms: 8.5 + x = -11.67261753 Solving 8.5 + x = -11.67261753 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 = -11.67261753 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.67261753 + -8.5 x = -11.67261753 + -8.5 Combine like terms: -11.67261753 + -8.5 = -20.17261753 x = -20.17261753 Simplifying x = -20.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17261753, -20.17261753}
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