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Simplifying x2 + -13x + 11 = 0 Reorder the terms: 11 + -13x + x2 = 0 Solving 11 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -13x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -13x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -13x + x2 = 0 + -11 -13x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -13x + x2 = -11 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 = -11 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -11 + 42.25 Combine like terms: -11 + 42.25 = 31.25 42.25 + -13x + x2 = 31.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -6.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -6.5 = 5.590169944 Simplifying x + -6.5 = 5.590169944 Reorder the terms: -6.5 + x = 5.590169944 Solving -6.5 + x = 5.590169944 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 = 5.590169944 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.590169944 + 6.5 x = 5.590169944 + 6.5 Combine like terms: 5.590169944 + 6.5 = 12.090169944 x = 12.090169944 Simplifying x = 12.090169944Subproblem 2
x + -6.5 = -5.590169944 Simplifying x + -6.5 = -5.590169944 Reorder the terms: -6.5 + x = -5.590169944 Solving -6.5 + x = -5.590169944 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 = -5.590169944 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.590169944 + 6.5 x = -5.590169944 + 6.5 Combine like terms: -5.590169944 + 6.5 = 0.909830056 x = 0.909830056 Simplifying x = 0.909830056Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.090169944, 0.909830056}
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