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Simplifying x2 + 11x = 15 Reorder the terms: 11x + x2 = 15 Solving 11x + x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 11x + x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 11x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 11x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 11x + x2 = 0 + 15 11x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 11x + x2 = 15 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 = 15 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 15 + 30.25 Combine like terms: 15 + 30.25 = 45.25 30.25 + 11x + x2 = 45.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 5.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 5.5 = 6.726812024 Simplifying x + 5.5 = 6.726812024 Reorder the terms: 5.5 + x = 6.726812024 Solving 5.5 + x = 6.726812024 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 = 6.726812024 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.726812024 + -5.5 x = 6.726812024 + -5.5 Combine like terms: 6.726812024 + -5.5 = 1.226812024 x = 1.226812024 Simplifying x = 1.226812024Subproblem 2
x + 5.5 = -6.726812024 Simplifying x + 5.5 = -6.726812024 Reorder the terms: 5.5 + x = -6.726812024 Solving 5.5 + x = -6.726812024 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 = -6.726812024 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.726812024 + -5.5 x = -6.726812024 + -5.5 Combine like terms: -6.726812024 + -5.5 = -12.226812024 x = -12.226812024 Simplifying x = -12.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.226812024, -12.226812024}
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