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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 = 12.226812024 x = 12.226812024 Simplifying x = 12.226812024Subproblem 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 = -1.226812024 x = -1.226812024 Simplifying x = -1.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.226812024, -1.226812024}
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