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Simplifying x2 + -13x + -18 = 0 Reorder the terms: -18 + -13x + x2 = 0 Solving -18 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -13x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -13x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -13x + x2 = 0 + 18 -13x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -13x + x2 = 18 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 = 18 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 18 + 42.25 Combine like terms: 18 + 42.25 = 60.25 42.25 + -13x + x2 = 60.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -6.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -6.5 = 7.762087348 Simplifying x + -6.5 = 7.762087348 Reorder the terms: -6.5 + x = 7.762087348 Solving -6.5 + x = 7.762087348 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 = 7.762087348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.762087348 + 6.5 x = 7.762087348 + 6.5 Combine like terms: 7.762087348 + 6.5 = 14.262087348 x = 14.262087348 Simplifying x = 14.262087348Subproblem 2
x + -6.5 = -7.762087348 Simplifying x + -6.5 = -7.762087348 Reorder the terms: -6.5 + x = -7.762087348 Solving -6.5 + x = -7.762087348 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 = -7.762087348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.762087348 + 6.5 x = -7.762087348 + 6.5 Combine like terms: -7.762087348 + 6.5 = -1.262087348 x = -1.262087348 Simplifying x = -1.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.262087348, -1.262087348}
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