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Simplifying x2 + x + -120 = 0 Reorder the terms: -120 + x + x2 = 0 Solving -120 + x + 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 + x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + x + x2 = 0 + 120 x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 x + x2 = 120 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 120 + 0.25 Reorder the terms: 0.25 + x + x2 = 120 + 0.25 Combine like terms: 120 + 0.25 = 120.25 0.25 + x + x2 = 120.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 0.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 0.5 = 10.9658561 Simplifying x + 0.5 = 10.9658561 Reorder the terms: 0.5 + x = 10.9658561 Solving 0.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.9658561 + -0.5 x = 10.9658561 + -0.5 Combine like terms: 10.9658561 + -0.5 = 10.4658561 x = 10.4658561 Simplifying x = 10.4658561Subproblem 2
x + 0.5 = -10.9658561 Simplifying x + 0.5 = -10.9658561 Reorder the terms: 0.5 + x = -10.9658561 Solving 0.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.9658561 + -0.5 x = -10.9658561 + -0.5 Combine like terms: -10.9658561 + -0.5 = -11.4658561 x = -11.4658561 Simplifying x = -11.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.4658561, -11.4658561}
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