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Simplifying 2X2 = -5X + 2 Reorder the terms: 2X2 = 2 + -5X Solving 2X2 = 2 + -5X Solving for variable 'X'. Reorder the terms: -2 + 5X + 2X2 = 2 + -5X + -2 + 5X Reorder the terms: -2 + 5X + 2X2 = 2 + -2 + -5X + 5X Combine like terms: 2 + -2 = 0 -2 + 5X + 2X2 = 0 + -5X + 5X -2 + 5X + 2X2 = -5X + 5X Combine like terms: -5X + 5X = 0 -2 + 5X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 2.5X + X2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.5X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 2.5X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.5X + X2 = 0 + 1 2.5X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.5X + X2 = 1 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 = 1 + 1.5625 Reorder the terms: 1.5625 + 2.5X + X2 = 1 + 1.5625 Combine like terms: 1 + 1.5625 = 2.5625 1.5625 + 2.5X + X2 = 2.5625 Factor a perfect square on the left side: (X + 1.25)(X + 1.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (X + 1.25) equal to 1.600781059 and -1.600781059.Subproblem 1
X + 1.25 = 1.600781059 Simplifying X + 1.25 = 1.600781059 Reorder the terms: 1.25 + X = 1.600781059 Solving 1.25 + X = 1.600781059 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 = 1.600781059 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 1.600781059 + -1.25 X = 1.600781059 + -1.25 Combine like terms: 1.600781059 + -1.25 = 0.350781059 X = 0.350781059 Simplifying X = 0.350781059Subproblem 2
X + 1.25 = -1.600781059 Simplifying X + 1.25 = -1.600781059 Reorder the terms: 1.25 + X = -1.600781059 Solving 1.25 + X = -1.600781059 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 = -1.600781059 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -1.600781059 + -1.25 X = -1.600781059 + -1.25 Combine like terms: -1.600781059 + -1.25 = -2.850781059 X = -2.850781059 Simplifying X = -2.850781059Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.350781059, -2.850781059}
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