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Simplifying x2 + -11x + -34 = 0 Reorder the terms: -34 + -11x + x2 = 0 Solving -34 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -11x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -11x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -11x + x2 = 0 + 34 -11x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -11x + x2 = 34 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 34 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 34 + 30.25 Combine like terms: 34 + 30.25 = 64.25 30.25 + -11x + x2 = 64.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -5.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + -5.5 = 8.015609771 Simplifying x + -5.5 = 8.015609771 Reorder the terms: -5.5 + x = 8.015609771 Solving -5.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 8.015609771 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.015609771 + 5.5 x = 8.015609771 + 5.5 Combine like terms: 8.015609771 + 5.5 = 13.515609771 x = 13.515609771 Simplifying x = 13.515609771Subproblem 2
x + -5.5 = -8.015609771 Simplifying x + -5.5 = -8.015609771 Reorder the terms: -5.5 + x = -8.015609771 Solving -5.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -8.015609771 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.015609771 + 5.5 x = -8.015609771 + 5.5 Combine like terms: -8.015609771 + 5.5 = -2.515609771 x = -2.515609771 Simplifying x = -2.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.515609771, -2.515609771}
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