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Simplifying 2X2 + -8X + -8 = X + -4 Reorder the terms: -8 + -8X + 2X2 = X + -4 Reorder the terms: -8 + -8X + 2X2 = -4 + X Solving -8 + -8X + 2X2 = -4 + X Solving for variable 'X'. Reorder the terms: -8 + 4 + -8X + -1X + 2X2 = -4 + X + 4 + -1X Combine like terms: -8 + 4 = -4 -4 + -8X + -1X + 2X2 = -4 + X + 4 + -1X Combine like terms: -8X + -1X = -9X -4 + -9X + 2X2 = -4 + X + 4 + -1X Reorder the terms: -4 + -9X + 2X2 = -4 + 4 + X + -1X Combine like terms: -4 + 4 = 0 -4 + -9X + 2X2 = 0 + X + -1X -4 + -9X + 2X2 = X + -1X Combine like terms: X + -1X = 0 -4 + -9X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -4.5X + X2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.5X + 2 + X2 = 0 + 2 Reorder the terms: -2 + 2 + -4.5X + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.5X + X2 = 0 + 2 -4.5X + X2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.5X + X2 = 2 The X term is -4.5X. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5X + 5.0625 + X2 = 2 + 5.0625 Reorder the terms: 5.0625 + -4.5X + X2 = 2 + 5.0625 Combine like terms: 2 + 5.0625 = 7.0625 5.0625 + -4.5X + X2 = 7.0625 Factor a perfect square on the left side: (X + -2.25)(X + -2.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (X + -2.25) equal to 2.657536453 and -2.657536453.Subproblem 1
X + -2.25 = 2.657536453 Simplifying X + -2.25 = 2.657536453 Reorder the terms: -2.25 + X = 2.657536453 Solving -2.25 + X = 2.657536453 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + X = 2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = 2.657536453 + 2.25 X = 2.657536453 + 2.25 Combine like terms: 2.657536453 + 2.25 = 4.907536453 X = 4.907536453 Simplifying X = 4.907536453Subproblem 2
X + -2.25 = -2.657536453 Simplifying X + -2.25 = -2.657536453 Reorder the terms: -2.25 + X = -2.657536453 Solving -2.25 + X = -2.657536453 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + X = -2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = -2.657536453 + 2.25 X = -2.657536453 + 2.25 Combine like terms: -2.657536453 + 2.25 = -0.407536453 X = -0.407536453 Simplifying X = -0.407536453Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.907536453, -0.407536453}
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