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Simplifying x2 + 11x = -26 Reorder the terms: 11x + x2 = -26 Solving 11x + x2 = -26 Solving for variable 'x'. Reorder the terms: 26 + 11x + x2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 11x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 11x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 11x + x2 = 0 + -26 11x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 11x + x2 = -26 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 = -26 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -26 + 30.25 Combine like terms: -26 + 30.25 = 4.25 30.25 + 11x + x2 = 4.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 5.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 5.5 = 2.061552813 Simplifying x + 5.5 = 2.061552813 Reorder the terms: 5.5 + x = 2.061552813 Solving 5.5 + x = 2.061552813 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 = 2.061552813 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 2.061552813 + -5.5 x = 2.061552813 + -5.5 Combine like terms: 2.061552813 + -5.5 = -3.438447187 x = -3.438447187 Simplifying x = -3.438447187Subproblem 2
x + 5.5 = -2.061552813 Simplifying x + 5.5 = -2.061552813 Reorder the terms: 5.5 + x = -2.061552813 Solving 5.5 + x = -2.061552813 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 = -2.061552813 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -2.061552813 + -5.5 x = -2.061552813 + -5.5 Combine like terms: -2.061552813 + -5.5 = -7.561552813 x = -7.561552813 Simplifying x = -7.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.438447187, -7.561552813}
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