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Simplifying x2 + -10x + -220 = 0 Reorder the terms: -220 + -10x + x2 = 0 Solving -220 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + -10x + 220 + x2 = 0 + 220 Reorder the terms: -220 + 220 + -10x + x2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -10x + x2 = 0 + 220 -10x + x2 = 0 + 220 Combine like terms: 0 + 220 = 220 -10x + x2 = 220 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 = 220 + 25 Reorder the terms: 25 + -10x + x2 = 220 + 25 Combine like terms: 220 + 25 = 245 25 + -10x + x2 = 245 Factor a perfect square on the left side: (x + -5)(x + -5) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (x + -5) equal to 15.652475842 and -15.652475842.Subproblem 1
x + -5 = 15.652475842 Simplifying x + -5 = 15.652475842 Reorder the terms: -5 + x = 15.652475842 Solving -5 + x = 15.652475842 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 = 15.652475842 + 5 Combine like terms: -5 + 5 = 0 0 + x = 15.652475842 + 5 x = 15.652475842 + 5 Combine like terms: 15.652475842 + 5 = 20.652475842 x = 20.652475842 Simplifying x = 20.652475842Subproblem 2
x + -5 = -15.652475842 Simplifying x + -5 = -15.652475842 Reorder the terms: -5 + x = -15.652475842 Solving -5 + x = -15.652475842 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 = -15.652475842 + 5 Combine like terms: -5 + 5 = 0 0 + x = -15.652475842 + 5 x = -15.652475842 + 5 Combine like terms: -15.652475842 + 5 = -10.652475842 x = -10.652475842 Simplifying x = -10.652475842Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.652475842, -10.652475842}
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