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Simplifying x2 + 23x + -120 = 0 Reorder the terms: -120 + 23x + x2 = 0 Solving -120 + 23x + 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 + 23x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 23x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 23x + x2 = 0 + 120 23x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 23x + x2 = 120 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 120 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 120 + 132.25 Combine like terms: 120 + 132.25 = 252.25 132.25 + 23x + x2 = 252.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + 11.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + 11.5 = 15.882380174 Simplifying x + 11.5 = 15.882380174 Reorder the terms: 11.5 + x = 15.882380174 Solving 11.5 + x = 15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 15.882380174 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 15.882380174 + -11.5 x = 15.882380174 + -11.5 Combine like terms: 15.882380174 + -11.5 = 4.382380174 x = 4.382380174 Simplifying x = 4.382380174Subproblem 2
x + 11.5 = -15.882380174 Simplifying x + 11.5 = -15.882380174 Reorder the terms: 11.5 + x = -15.882380174 Solving 11.5 + x = -15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -15.882380174 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -15.882380174 + -11.5 x = -15.882380174 + -11.5 Combine like terms: -15.882380174 + -11.5 = -27.382380174 x = -27.382380174 Simplifying x = -27.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.382380174, -27.382380174}
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