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Simplifying x2 + 24x + -5 = 0 Reorder the terms: -5 + 24x + x2 = 0 Solving -5 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 24x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 24x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 24x + x2 = 0 + 5 24x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 24x + x2 = 5 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 = 5 + 144 Reorder the terms: 144 + 24x + x2 = 5 + 144 Combine like terms: 5 + 144 = 149 144 + 24x + x2 = 149 Factor a perfect square on the left side: (x + 12)(x + 12) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + 12) equal to 12.206555616 and -12.206555616.Subproblem 1
x + 12 = 12.206555616 Simplifying x + 12 = 12.206555616 Reorder the terms: 12 + x = 12.206555616 Solving 12 + x = 12.206555616 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 = 12.206555616 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.206555616 + -12 x = 12.206555616 + -12 Combine like terms: 12.206555616 + -12 = 0.206555616 x = 0.206555616 Simplifying x = 0.206555616Subproblem 2
x + 12 = -12.206555616 Simplifying x + 12 = -12.206555616 Reorder the terms: 12 + x = -12.206555616 Solving 12 + x = -12.206555616 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 = -12.206555616 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.206555616 + -12 x = -12.206555616 + -12 Combine like terms: -12.206555616 + -12 = -24.206555616 x = -24.206555616 Simplifying x = -24.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.206555616, -24.206555616}
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