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Simplifying x(x + -17) + 27 = 0 Reorder the terms: x(-17 + x) + 27 = 0 (-17 * x + x * x) + 27 = 0 (-17x + x2) + 27 = 0 Reorder the terms: 27 + -17x + x2 = 0 Solving 27 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -17x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -17x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -17x + x2 = 0 + -27 -17x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -17x + x2 = -27 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 = -27 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -27 + 72.25 Combine like terms: -27 + 72.25 = 45.25 72.25 + -17x + x2 = 45.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -8.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -8.5 = 6.726812024 Simplifying x + -8.5 = 6.726812024 Reorder the terms: -8.5 + x = 6.726812024 Solving -8.5 + x = 6.726812024 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 = 6.726812024 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 6.726812024 + 8.5 x = 6.726812024 + 8.5 Combine like terms: 6.726812024 + 8.5 = 15.226812024 x = 15.226812024 Simplifying x = 15.226812024Subproblem 2
x + -8.5 = -6.726812024 Simplifying x + -8.5 = -6.726812024 Reorder the terms: -8.5 + x = -6.726812024 Solving -8.5 + x = -6.726812024 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 = -6.726812024 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -6.726812024 + 8.5 x = -6.726812024 + 8.5 Combine like terms: -6.726812024 + 8.5 = 1.773187976 x = 1.773187976 Simplifying x = 1.773187976Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.226812024, 1.773187976}
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