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Simplifying X2 + 37X + -1100 = 0 Reorder the terms: -1100 + 37X + X2 = 0 Solving -1100 + 37X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + 37X + 1100 + X2 = 0 + 1100 Reorder the terms: -1100 + 1100 + 37X + X2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + 37X + X2 = 0 + 1100 37X + X2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 37X + X2 = 1100 The X term is 37X. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37X + 342.25 + X2 = 1100 + 342.25 Reorder the terms: 342.25 + 37X + X2 = 1100 + 342.25 Combine like terms: 1100 + 342.25 = 1442.25 342.25 + 37X + X2 = 1442.25 Factor a perfect square on the left side: (X + 18.5)(X + 18.5) = 1442.25 Calculate the square root of the right side: 37.976966704 Break this problem into two subproblems by setting (X + 18.5) equal to 37.976966704 and -37.976966704.Subproblem 1
X + 18.5 = 37.976966704 Simplifying X + 18.5 = 37.976966704 Reorder the terms: 18.5 + X = 37.976966704 Solving 18.5 + X = 37.976966704 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + X = 37.976966704 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + X = 37.976966704 + -18.5 X = 37.976966704 + -18.5 Combine like terms: 37.976966704 + -18.5 = 19.476966704 X = 19.476966704 Simplifying X = 19.476966704Subproblem 2
X + 18.5 = -37.976966704 Simplifying X + 18.5 = -37.976966704 Reorder the terms: 18.5 + X = -37.976966704 Solving 18.5 + X = -37.976966704 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + X = -37.976966704 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + X = -37.976966704 + -18.5 X = -37.976966704 + -18.5 Combine like terms: -37.976966704 + -18.5 = -56.476966704 X = -56.476966704 Simplifying X = -56.476966704Solution
The solution to the problem is based on the solutions from the subproblems. X = {19.476966704, -56.476966704}
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