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Simplifying 11x + x2 = 144 Solving 11x + x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 11x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 11x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 11x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 11x + x2 = 0 + 144 11x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 11x + x2 = 144 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 = 144 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 144 + 30.25 Combine like terms: 144 + 30.25 = 174.25 30.25 + 11x + x2 = 174.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + 5.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + 5.5 = 13.200378782 Simplifying x + 5.5 = 13.200378782 Reorder the terms: 5.5 + x = 13.200378782 Solving 5.5 + x = 13.200378782 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 = 13.200378782 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 13.200378782 + -5.5 x = 13.200378782 + -5.5 Combine like terms: 13.200378782 + -5.5 = 7.700378782 x = 7.700378782 Simplifying x = 7.700378782Subproblem 2
x + 5.5 = -13.200378782 Simplifying x + 5.5 = -13.200378782 Reorder the terms: 5.5 + x = -13.200378782 Solving 5.5 + x = -13.200378782 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 = -13.200378782 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -13.200378782 + -5.5 x = -13.200378782 + -5.5 Combine like terms: -13.200378782 + -5.5 = -18.700378782 x = -18.700378782 Simplifying x = -18.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.700378782, -18.700378782}
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