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Simplifying 2X2 + -5X = 37 Reorder the terms: -5X + 2X2 = 37 Solving -5X + 2X2 = 37 Solving for variable 'X'. Reorder the terms: -37 + -5X + 2X2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -5X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18.5 + -2.5X + X2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -2.5X + 18.5 + X2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -2.5X + X2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -2.5X + X2 = 0 + 18.5 -2.5X + X2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -2.5X + X2 = 18.5 The X term is -2.5X. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5X + 1.5625 + X2 = 18.5 + 1.5625 Reorder the terms: 1.5625 + -2.5X + X2 = 18.5 + 1.5625 Combine like terms: 18.5 + 1.5625 = 20.0625 1.5625 + -2.5X + X2 = 20.0625 Factor a perfect square on the left side: (X + -1.25)(X + -1.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (X + -1.25) equal to 4.479118217 and -4.479118217.Subproblem 1
X + -1.25 = 4.479118217 Simplifying X + -1.25 = 4.479118217 Reorder the terms: -1.25 + X = 4.479118217 Solving -1.25 + X = 4.479118217 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = 4.479118217 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = 4.479118217 + 1.25 X = 4.479118217 + 1.25 Combine like terms: 4.479118217 + 1.25 = 5.729118217 X = 5.729118217 Simplifying X = 5.729118217Subproblem 2
X + -1.25 = -4.479118217 Simplifying X + -1.25 = -4.479118217 Reorder the terms: -1.25 + X = -4.479118217 Solving -1.25 + X = -4.479118217 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = -4.479118217 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = -4.479118217 + 1.25 X = -4.479118217 + 1.25 Combine like terms: -4.479118217 + 1.25 = -3.229118217 X = -3.229118217 Simplifying X = -3.229118217Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.729118217, -3.229118217}
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