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Simplifying x2 + 119x + 120 = 0 Reorder the terms: 120 + 119x + x2 = 0 Solving 120 + 119x + 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 + 119x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 119x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 119x + x2 = 0 + -120 119x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 119x + x2 = -120 The x term is 119x. Take half its coefficient (59.5). Square it (3540.25) and add it to both sides. Add '3540.25' to each side of the equation. 119x + 3540.25 + x2 = -120 + 3540.25 Reorder the terms: 3540.25 + 119x + x2 = -120 + 3540.25 Combine like terms: -120 + 3540.25 = 3420.25 3540.25 + 119x + x2 = 3420.25 Factor a perfect square on the left side: (x + 59.5)(x + 59.5) = 3420.25 Calculate the square root of the right side: 58.482903485 Break this problem into two subproblems by setting (x + 59.5) equal to 58.482903485 and -58.482903485.Subproblem 1
x + 59.5 = 58.482903485 Simplifying x + 59.5 = 58.482903485 Reorder the terms: 59.5 + x = 58.482903485 Solving 59.5 + x = 58.482903485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59.5' to each side of the equation. 59.5 + -59.5 + x = 58.482903485 + -59.5 Combine like terms: 59.5 + -59.5 = 0.0 0.0 + x = 58.482903485 + -59.5 x = 58.482903485 + -59.5 Combine like terms: 58.482903485 + -59.5 = -1.017096515 x = -1.017096515 Simplifying x = -1.017096515Subproblem 2
x + 59.5 = -58.482903485 Simplifying x + 59.5 = -58.482903485 Reorder the terms: 59.5 + x = -58.482903485 Solving 59.5 + x = -58.482903485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59.5' to each side of the equation. 59.5 + -59.5 + x = -58.482903485 + -59.5 Combine like terms: 59.5 + -59.5 = 0.0 0.0 + x = -58.482903485 + -59.5 x = -58.482903485 + -59.5 Combine like terms: -58.482903485 + -59.5 = -117.982903485 x = -117.982903485 Simplifying x = -117.982903485Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.017096515, -117.982903485}
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