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Simplifying x2 + 24x + 2 = 0 Reorder the terms: 2 + 24x + x2 = 0 Solving 2 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 24x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 24x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 24x + x2 = 0 + -2 24x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 24x + x2 = -2 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -2 + 144 Reorder the terms: 144 + 24x + x2 = -2 + 144 Combine like terms: -2 + 144 = 142 144 + 24x + x2 = 142 Factor a perfect square on the left side: (x + 12)(x + 12) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (x + 12) equal to 11.916375288 and -11.916375288.Subproblem 1
x + 12 = 11.916375288 Simplifying x + 12 = 11.916375288 Reorder the terms: 12 + x = 11.916375288 Solving 12 + x = 11.916375288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 11.916375288 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.916375288 + -12 x = 11.916375288 + -12 Combine like terms: 11.916375288 + -12 = -0.083624712 x = -0.083624712 Simplifying x = -0.083624712Subproblem 2
x + 12 = -11.916375288 Simplifying x + 12 = -11.916375288 Reorder the terms: 12 + x = -11.916375288 Solving 12 + x = -11.916375288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -11.916375288 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.916375288 + -12 x = -11.916375288 + -12 Combine like terms: -11.916375288 + -12 = -23.916375288 x = -23.916375288 Simplifying x = -23.916375288Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.083624712, -23.916375288}
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