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Simplifying x2 + 10x + -244 = 0 Reorder the terms: -244 + 10x + x2 = 0 Solving -244 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '244' to each side of the equation. -244 + 10x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + 10x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + 10x + x2 = 0 + 244 10x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 10x + x2 = 244 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 = 244 + 25 Reorder the terms: 25 + 10x + x2 = 244 + 25 Combine like terms: 244 + 25 = 269 25 + 10x + x2 = 269 Factor a perfect square on the left side: (x + 5)(x + 5) = 269 Calculate the square root of the right side: 16.401219467 Break this problem into two subproblems by setting (x + 5) equal to 16.401219467 and -16.401219467.Subproblem 1
x + 5 = 16.401219467 Simplifying x + 5 = 16.401219467 Reorder the terms: 5 + x = 16.401219467 Solving 5 + x = 16.401219467 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 = 16.401219467 + -5 Combine like terms: 5 + -5 = 0 0 + x = 16.401219467 + -5 x = 16.401219467 + -5 Combine like terms: 16.401219467 + -5 = 11.401219467 x = 11.401219467 Simplifying x = 11.401219467Subproblem 2
x + 5 = -16.401219467 Simplifying x + 5 = -16.401219467 Reorder the terms: 5 + x = -16.401219467 Solving 5 + x = -16.401219467 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 = -16.401219467 + -5 Combine like terms: 5 + -5 = 0 0 + x = -16.401219467 + -5 x = -16.401219467 + -5 Combine like terms: -16.401219467 + -5 = -21.401219467 x = -21.401219467 Simplifying x = -21.401219467Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.401219467, -21.401219467}
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