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Simplifying X2 + 24X + 50 = 42 Reorder the terms: 50 + 24X + X2 = 42 Solving 50 + 24X + X2 = 42 Solving for variable 'X'. Reorder the terms: 50 + -42 + 24X + X2 = 42 + -42 Combine like terms: 50 + -42 = 8 8 + 24X + X2 = 42 + -42 Combine like terms: 42 + -42 = 0 8 + 24X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 24X + -8 + X2 = 0 + -8 Reorder the terms: 8 + -8 + 24X + X2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 24X + X2 = 0 + -8 24X + X2 = 0 + -8 Combine like terms: 0 + -8 = -8 24X + X2 = -8 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 = -8 + 144 Reorder the terms: 144 + 24X + X2 = -8 + 144 Combine like terms: -8 + 144 = 136 144 + 24X + X2 = 136 Factor a perfect square on the left side: (X + 12)(X + 12) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (X + 12) equal to 11.66190379 and -11.66190379.Subproblem 1
X + 12 = 11.66190379 Simplifying X + 12 = 11.66190379 Reorder the terms: 12 + X = 11.66190379 Solving 12 + X = 11.66190379 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 = 11.66190379 + -12 Combine like terms: 12 + -12 = 0 0 + X = 11.66190379 + -12 X = 11.66190379 + -12 Combine like terms: 11.66190379 + -12 = -0.33809621 X = -0.33809621 Simplifying X = -0.33809621Subproblem 2
X + 12 = -11.66190379 Simplifying X + 12 = -11.66190379 Reorder the terms: 12 + X = -11.66190379 Solving 12 + X = -11.66190379 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 = -11.66190379 + -12 Combine like terms: 12 + -12 = 0 0 + X = -11.66190379 + -12 X = -11.66190379 + -12 Combine like terms: -11.66190379 + -12 = -23.66190379 X = -23.66190379 Simplifying X = -23.66190379Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.33809621, -23.66190379}
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