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Simplifying 2X2 + -49X = 360 Reorder the terms: -49X + 2X2 = 360 Solving -49X + 2X2 = 360 Solving for variable 'X'. Reorder the terms: -360 + -49X + 2X2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + -49X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -180 + -24.5X + X2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + -24.5X + 180 + X2 = 0 + 180 Reorder the terms: -180 + 180 + -24.5X + X2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -24.5X + X2 = 0 + 180 -24.5X + X2 = 0 + 180 Combine like terms: 0 + 180 = 180 -24.5X + X2 = 180 The X term is -24.5X. Take half its coefficient (-12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. -24.5X + 150.0625 + X2 = 180 + 150.0625 Reorder the terms: 150.0625 + -24.5X + X2 = 180 + 150.0625 Combine like terms: 180 + 150.0625 = 330.0625 150.0625 + -24.5X + X2 = 330.0625 Factor a perfect square on the left side: (X + -12.25)(X + -12.25) = 330.0625 Calculate the square root of the right side: 18.167622299 Break this problem into two subproblems by setting (X + -12.25) equal to 18.167622299 and -18.167622299.Subproblem 1
X + -12.25 = 18.167622299 Simplifying X + -12.25 = 18.167622299 Reorder the terms: -12.25 + X = 18.167622299 Solving -12.25 + X = 18.167622299 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + X = 18.167622299 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + X = 18.167622299 + 12.25 X = 18.167622299 + 12.25 Combine like terms: 18.167622299 + 12.25 = 30.417622299 X = 30.417622299 Simplifying X = 30.417622299Subproblem 2
X + -12.25 = -18.167622299 Simplifying X + -12.25 = -18.167622299 Reorder the terms: -12.25 + X = -18.167622299 Solving -12.25 + X = -18.167622299 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + X = -18.167622299 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + X = -18.167622299 + 12.25 X = -18.167622299 + 12.25 Combine like terms: -18.167622299 + 12.25 = -5.917622299 X = -5.917622299 Simplifying X = -5.917622299Solution
The solution to the problem is based on the solutions from the subproblems. X = {30.417622299, -5.917622299}
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