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Simplifying x2 + 10x + -120 = 0 Reorder the terms: -120 + 10x + x2 = 0 Solving -120 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 10x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 10x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 10x + x2 = 0 + 120 10x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 10x + x2 = 120 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 = 120 + 25 Reorder the terms: 25 + 10x + x2 = 120 + 25 Combine like terms: 120 + 25 = 145 25 + 10x + x2 = 145 Factor a perfect square on the left side: (x + 5)(x + 5) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 5) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 5 = 12.041594579 Simplifying x + 5 = 12.041594579 Reorder the terms: 5 + x = 12.041594579 Solving 5 + x = 12.041594579 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 = 12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.041594579 + -5 x = 12.041594579 + -5 Combine like terms: 12.041594579 + -5 = 7.041594579 x = 7.041594579 Simplifying x = 7.041594579Subproblem 2
x + 5 = -12.041594579 Simplifying x + 5 = -12.041594579 Reorder the terms: 5 + x = -12.041594579 Solving 5 + x = -12.041594579 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 = -12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.041594579 + -5 x = -12.041594579 + -5 Combine like terms: -12.041594579 + -5 = -17.041594579 x = -17.041594579 Simplifying x = -17.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.041594579, -17.041594579}
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