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Simplifying x2 + -13x + -8185 = 0 Reorder the terms: -8185 + -13x + x2 = 0 Solving -8185 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8185' to each side of the equation. -8185 + -13x + 8185 + x2 = 0 + 8185 Reorder the terms: -8185 + 8185 + -13x + x2 = 0 + 8185 Combine like terms: -8185 + 8185 = 0 0 + -13x + x2 = 0 + 8185 -13x + x2 = 0 + 8185 Combine like terms: 0 + 8185 = 8185 -13x + x2 = 8185 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 8185 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 8185 + 42.25 Combine like terms: 8185 + 42.25 = 8227.25 42.25 + -13x + x2 = 8227.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 8227.25 Calculate the square root of the right side: 90.704189539 Break this problem into two subproblems by setting (x + -6.5) equal to 90.704189539 and -90.704189539.Subproblem 1
x + -6.5 = 90.704189539 Simplifying x + -6.5 = 90.704189539 Reorder the terms: -6.5 + x = 90.704189539 Solving -6.5 + x = 90.704189539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 90.704189539 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 90.704189539 + 6.5 x = 90.704189539 + 6.5 Combine like terms: 90.704189539 + 6.5 = 97.204189539 x = 97.204189539 Simplifying x = 97.204189539Subproblem 2
x + -6.5 = -90.704189539 Simplifying x + -6.5 = -90.704189539 Reorder the terms: -6.5 + x = -90.704189539 Solving -6.5 + x = -90.704189539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -90.704189539 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -90.704189539 + 6.5 x = -90.704189539 + 6.5 Combine like terms: -90.704189539 + 6.5 = -84.204189539 x = -84.204189539 Simplifying x = -84.204189539Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.204189539, -84.204189539}
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