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Simplifying x2 + 10x + -110 = 0 Reorder the terms: -110 + 10x + x2 = 0 Solving -110 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 10x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 10x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 10x + x2 = 0 + 110 10x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 10x + x2 = 110 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 110 + 25 Reorder the terms: 25 + 10x + x2 = 110 + 25 Combine like terms: 110 + 25 = 135 25 + 10x + x2 = 135 Factor a perfect square on the left side: (x + 5)(x + 5) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + 5) equal to 11.618950039 and -11.618950039.Subproblem 1
x + 5 = 11.618950039 Simplifying x + 5 = 11.618950039 Reorder the terms: 5 + x = 11.618950039 Solving 5 + x = 11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.618950039 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.618950039 + -5 x = 11.618950039 + -5 Combine like terms: 11.618950039 + -5 = 6.618950039 x = 6.618950039 Simplifying x = 6.618950039Subproblem 2
x + 5 = -11.618950039 Simplifying x + 5 = -11.618950039 Reorder the terms: 5 + x = -11.618950039 Solving 5 + x = -11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.618950039 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.618950039 + -5 x = -11.618950039 + -5 Combine like terms: -11.618950039 + -5 = -16.618950039 x = -16.618950039 Simplifying x = -16.618950039Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.618950039, -16.618950039}
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