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Simplifying 2X2 + -9X + -88 = 0 Reorder the terms: -88 + -9X + 2X2 = 0 Solving -88 + -9X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -44 + -4.5X + X2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -4.5X + 44 + X2 = 0 + 44 Reorder the terms: -44 + 44 + -4.5X + X2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -4.5X + X2 = 0 + 44 -4.5X + X2 = 0 + 44 Combine like terms: 0 + 44 = 44 -4.5X + X2 = 44 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 = 44 + 5.0625 Reorder the terms: 5.0625 + -4.5X + X2 = 44 + 5.0625 Combine like terms: 44 + 5.0625 = 49.0625 5.0625 + -4.5X + X2 = 49.0625 Factor a perfect square on the left side: (X + -2.25)(X + -2.25) = 49.0625 Calculate the square root of the right side: 7.004462863 Break this problem into two subproblems by setting (X + -2.25) equal to 7.004462863 and -7.004462863.Subproblem 1
X + -2.25 = 7.004462863 Simplifying X + -2.25 = 7.004462863 Reorder the terms: -2.25 + X = 7.004462863 Solving -2.25 + X = 7.004462863 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 = 7.004462863 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = 7.004462863 + 2.25 X = 7.004462863 + 2.25 Combine like terms: 7.004462863 + 2.25 = 9.254462863 X = 9.254462863 Simplifying X = 9.254462863Subproblem 2
X + -2.25 = -7.004462863 Simplifying X + -2.25 = -7.004462863 Reorder the terms: -2.25 + X = -7.004462863 Solving -2.25 + X = -7.004462863 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 = -7.004462863 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = -7.004462863 + 2.25 X = -7.004462863 + 2.25 Combine like terms: -7.004462863 + 2.25 = -4.754462863 X = -4.754462863 Simplifying X = -4.754462863Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.254462863, -4.754462863}
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