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Simplifying x2 + 24x + -60 = 0 Reorder the terms: -60 + 24x + x2 = 0 Solving -60 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 24x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 24x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 24x + x2 = 0 + 60 24x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 24x + x2 = 60 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 = 60 + 144 Reorder the terms: 144 + 24x + x2 = 60 + 144 Combine like terms: 60 + 144 = 204 144 + 24x + x2 = 204 Factor a perfect square on the left side: (x + 12)(x + 12) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 12) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 12 = 14.282856857 Simplifying x + 12 = 14.282856857 Reorder the terms: 12 + x = 14.282856857 Solving 12 + x = 14.282856857 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 = 14.282856857 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.282856857 + -12 x = 14.282856857 + -12 Combine like terms: 14.282856857 + -12 = 2.282856857 x = 2.282856857 Simplifying x = 2.282856857Subproblem 2
x + 12 = -14.282856857 Simplifying x + 12 = -14.282856857 Reorder the terms: 12 + x = -14.282856857 Solving 12 + x = -14.282856857 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 = -14.282856857 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.282856857 + -12 x = -14.282856857 + -12 Combine like terms: -14.282856857 + -12 = -26.282856857 x = -26.282856857 Simplifying x = -26.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.282856857, -26.282856857}
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