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Simplifying x2 + 24x + -5184 = 0 Reorder the terms: -5184 + 24x + x2 = 0 Solving -5184 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5184' to each side of the equation. -5184 + 24x + 5184 + x2 = 0 + 5184 Reorder the terms: -5184 + 5184 + 24x + x2 = 0 + 5184 Combine like terms: -5184 + 5184 = 0 0 + 24x + x2 = 0 + 5184 24x + x2 = 0 + 5184 Combine like terms: 0 + 5184 = 5184 24x + x2 = 5184 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 = 5184 + 144 Reorder the terms: 144 + 24x + x2 = 5184 + 144 Combine like terms: 5184 + 144 = 5328 144 + 24x + x2 = 5328 Factor a perfect square on the left side: (x + 12)(x + 12) = 5328 Calculate the square root of the right side: 72.993150364 Break this problem into two subproblems by setting (x + 12) equal to 72.993150364 and -72.993150364.Subproblem 1
x + 12 = 72.993150364 Simplifying x + 12 = 72.993150364 Reorder the terms: 12 + x = 72.993150364 Solving 12 + x = 72.993150364 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 = 72.993150364 + -12 Combine like terms: 12 + -12 = 0 0 + x = 72.993150364 + -12 x = 72.993150364 + -12 Combine like terms: 72.993150364 + -12 = 60.993150364 x = 60.993150364 Simplifying x = 60.993150364Subproblem 2
x + 12 = -72.993150364 Simplifying x + 12 = -72.993150364 Reorder the terms: 12 + x = -72.993150364 Solving 12 + x = -72.993150364 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 = -72.993150364 + -12 Combine like terms: 12 + -12 = 0 0 + x = -72.993150364 + -12 x = -72.993150364 + -12 Combine like terms: -72.993150364 + -12 = -84.993150364 x = -84.993150364 Simplifying x = -84.993150364Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.993150364, -84.993150364}
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