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Simplifying 0 = x2 + 11x + -34 Reorder the terms: 0 = -34 + 11x + x2 Solving 0 = -34 + 11x + x2 Solving for variable 'x'. Combine like terms: 0 + 34 = 34 34 + -11x + -1x2 = -34 + 11x + x2 + 34 + -11x + -1x2 Reorder the terms: 34 + -11x + -1x2 = -34 + 34 + 11x + -11x + x2 + -1x2 Combine like terms: -34 + 34 = 0 34 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2 34 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 34 + -11x + -1x2 = 0 + x2 + -1x2 34 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 34 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + 11x + x2 = 0 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 = 2.515609771 x = 2.515609771 Simplifying x = 2.515609771Subproblem 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 = -13.515609771 x = -13.515609771 Simplifying x = -13.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.515609771, -13.515609771}
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