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Simplifying x2 + 11x = 154 Reorder the terms: 11x + x2 = 154 Solving 11x + x2 = 154 Solving for variable 'x'. Reorder the terms: -154 + 11x + x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -154 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '154' to each side of the equation. -154 + 11x + 154 + x2 = 0 + 154 Reorder the terms: -154 + 154 + 11x + x2 = 0 + 154 Combine like terms: -154 + 154 = 0 0 + 11x + x2 = 0 + 154 11x + x2 = 0 + 154 Combine like terms: 0 + 154 = 154 11x + x2 = 154 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 = 154 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 154 + 30.25 Combine like terms: 154 + 30.25 = 184.25 30.25 + 11x + x2 = 184.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 184.25 Calculate the square root of the right side: 13.57387196 Break this problem into two subproblems by setting (x + 5.5) equal to 13.57387196 and -13.57387196.Subproblem 1
x + 5.5 = 13.57387196 Simplifying x + 5.5 = 13.57387196 Reorder the terms: 5.5 + x = 13.57387196 Solving 5.5 + x = 13.57387196 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 = 13.57387196 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 13.57387196 + -5.5 x = 13.57387196 + -5.5 Combine like terms: 13.57387196 + -5.5 = 8.07387196 x = 8.07387196 Simplifying x = 8.07387196Subproblem 2
x + 5.5 = -13.57387196 Simplifying x + 5.5 = -13.57387196 Reorder the terms: 5.5 + x = -13.57387196 Solving 5.5 + x = -13.57387196 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 = -13.57387196 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -13.57387196 + -5.5 x = -13.57387196 + -5.5 Combine like terms: -13.57387196 + -5.5 = -19.07387196 x = -19.07387196 Simplifying x = -19.07387196Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.07387196, -19.07387196}
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