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Simplifying x2 + 10x + -124 = 0 Reorder the terms: -124 + 10x + x2 = 0 Solving -124 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 10x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 10x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 10x + x2 = 0 + 124 10x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 10x + x2 = 124 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 = 124 + 25 Reorder the terms: 25 + 10x + x2 = 124 + 25 Combine like terms: 124 + 25 = 149 25 + 10x + x2 = 149 Factor a perfect square on the left side: (x + 5)(x + 5) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + 5) equal to 12.206555616 and -12.206555616.Subproblem 1
x + 5 = 12.206555616 Simplifying x + 5 = 12.206555616 Reorder the terms: 5 + x = 12.206555616 Solving 5 + x = 12.206555616 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 = 12.206555616 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.206555616 + -5 x = 12.206555616 + -5 Combine like terms: 12.206555616 + -5 = 7.206555616 x = 7.206555616 Simplifying x = 7.206555616Subproblem 2
x + 5 = -12.206555616 Simplifying x + 5 = -12.206555616 Reorder the terms: 5 + x = -12.206555616 Solving 5 + x = -12.206555616 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 = -12.206555616 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.206555616 + -5 x = -12.206555616 + -5 Combine like terms: -12.206555616 + -5 = -17.206555616 x = -17.206555616 Simplifying x = -17.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.206555616, -17.206555616}
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