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Simplifying x2 + 11x = 50.75 Reorder the terms: 11x + x2 = 50.75 Solving 11x + x2 = 50.75 Solving for variable 'x'. Reorder the terms: -50.75 + 11x + x2 = 50.75 + -50.75 Combine like terms: 50.75 + -50.75 = 0.00 -50.75 + 11x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '50.75' to each side of the equation. -50.75 + 11x + 50.75 + x2 = 0.00 + 50.75 Reorder the terms: -50.75 + 50.75 + 11x + x2 = 0.00 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + 11x + x2 = 0.00 + 50.75 11x + x2 = 0.00 + 50.75 Combine like terms: 0.00 + 50.75 = 50.75 11x + x2 = 50.75 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 = 50.75 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 50.75 + 30.25 Combine like terms: 50.75 + 30.25 = 81 30.25 + 11x + x2 = 81 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (x + 5.5) equal to 9 and -9.Subproblem 1
x + 5.5 = 9 Simplifying x + 5.5 = 9 Reorder the terms: 5.5 + x = 9 Solving 5.5 + x = 9 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 = 9 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9 + -5.5 x = 9 + -5.5 Combine like terms: 9 + -5.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 5.5 = -9 Simplifying x + 5.5 = -9 Reorder the terms: 5.5 + x = -9 Solving 5.5 + x = -9 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 = -9 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9 + -5.5 x = -9 + -5.5 Combine like terms: -9 + -5.5 = -14.5 x = -14.5 Simplifying x = -14.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -14.5}
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