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Simplifying x2 + -13x + -8 = 0 Reorder the terms: -8 + -13x + x2 = 0 Solving -8 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -13x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -13x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -13x + x2 = 0 + 8 -13x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -13x + x2 = 8 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 = 8 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 8 + 42.25 Combine like terms: 8 + 42.25 = 50.25 42.25 + -13x + x2 = 50.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -6.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -6.5 = 7.088723439 Simplifying x + -6.5 = 7.088723439 Reorder the terms: -6.5 + x = 7.088723439 Solving -6.5 + x = 7.088723439 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 = 7.088723439 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.088723439 + 6.5 x = 7.088723439 + 6.5 Combine like terms: 7.088723439 + 6.5 = 13.588723439 x = 13.588723439 Simplifying x = 13.588723439Subproblem 2
x + -6.5 = -7.088723439 Simplifying x + -6.5 = -7.088723439 Reorder the terms: -6.5 + x = -7.088723439 Solving -6.5 + x = -7.088723439 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 = -7.088723439 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.088723439 + 6.5 x = -7.088723439 + 6.5 Combine like terms: -7.088723439 + 6.5 = -0.588723439 x = -0.588723439 Simplifying x = -0.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.588723439, -0.588723439}
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