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Simplifying x2 + 118x + -120 = 0 Reorder the terms: -120 + 118x + x2 = 0 Solving -120 + 118x + 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 + 118x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 118x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 118x + x2 = 0 + 120 118x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 118x + x2 = 120 The x term is 118x. Take half its coefficient (59). Square it (3481) and add it to both sides. Add '3481' to each side of the equation. 118x + 3481 + x2 = 120 + 3481 Reorder the terms: 3481 + 118x + x2 = 120 + 3481 Combine like terms: 120 + 3481 = 3601 3481 + 118x + x2 = 3601 Factor a perfect square on the left side: (x + 59)(x + 59) = 3601 Calculate the square root of the right side: 60.008332755 Break this problem into two subproblems by setting (x + 59) equal to 60.008332755 and -60.008332755.Subproblem 1
x + 59 = 60.008332755 Simplifying x + 59 = 60.008332755 Reorder the terms: 59 + x = 60.008332755 Solving 59 + x = 60.008332755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = 60.008332755 + -59 Combine like terms: 59 + -59 = 0 0 + x = 60.008332755 + -59 x = 60.008332755 + -59 Combine like terms: 60.008332755 + -59 = 1.008332755 x = 1.008332755 Simplifying x = 1.008332755Subproblem 2
x + 59 = -60.008332755 Simplifying x + 59 = -60.008332755 Reorder the terms: 59 + x = -60.008332755 Solving 59 + x = -60.008332755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = -60.008332755 + -59 Combine like terms: 59 + -59 = 0 0 + x = -60.008332755 + -59 x = -60.008332755 + -59 Combine like terms: -60.008332755 + -59 = -119.008332755 x = -119.008332755 Simplifying x = -119.008332755Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.008332755, -119.008332755}
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