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Simplifying x2 + -39x + -169 = 0 Reorder the terms: -169 + -39x + x2 = 0 Solving -169 + -39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + -39x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + -39x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + -39x + x2 = 0 + 169 -39x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 -39x + x2 = 169 The x term is -39x. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x + 380.25 + x2 = 169 + 380.25 Reorder the terms: 380.25 + -39x + x2 = 169 + 380.25 Combine like terms: 169 + 380.25 = 549.25 380.25 + -39x + x2 = 549.25 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 549.25 Calculate the square root of the right side: 23.436083291 Break this problem into two subproblems by setting (x + -19.5) equal to 23.436083291 and -23.436083291.Subproblem 1
x + -19.5 = 23.436083291 Simplifying x + -19.5 = 23.436083291 Reorder the terms: -19.5 + x = 23.436083291 Solving -19.5 + x = 23.436083291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 23.436083291 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 23.436083291 + 19.5 x = 23.436083291 + 19.5 Combine like terms: 23.436083291 + 19.5 = 42.936083291 x = 42.936083291 Simplifying x = 42.936083291Subproblem 2
x + -19.5 = -23.436083291 Simplifying x + -19.5 = -23.436083291 Reorder the terms: -19.5 + x = -23.436083291 Solving -19.5 + x = -23.436083291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -23.436083291 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -23.436083291 + 19.5 x = -23.436083291 + 19.5 Combine like terms: -23.436083291 + 19.5 = -3.936083291 x = -3.936083291 Simplifying x = -3.936083291Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.936083291, -3.936083291}
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