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Simplifying 0 = 2X2 + -3X + -36 Reorder the terms: 0 = -36 + -3X + 2X2 Solving 0 = -36 + -3X + 2X2 Solving for variable 'X'. Combine like terms: 0 + 36 = 36 36 + 3X + -2X2 = -36 + -3X + 2X2 + 36 + 3X + -2X2 Reorder the terms: 36 + 3X + -2X2 = -36 + 36 + -3X + 3X + 2X2 + -2X2 Combine like terms: -36 + 36 = 0 36 + 3X + -2X2 = 0 + -3X + 3X + 2X2 + -2X2 36 + 3X + -2X2 = -3X + 3X + 2X2 + -2X2 Combine like terms: -3X + 3X = 0 36 + 3X + -2X2 = 0 + 2X2 + -2X2 36 + 3X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 36 + 3X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -18 + -1.5X + X2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -1.5X + 18 + X2 = 0 + 18 Reorder the terms: -18 + 18 + -1.5X + X2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1.5X + X2 = 0 + 18 -1.5X + X2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1.5X + X2 = 18 The X term is -1.5X. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5X + 0.5625 + X2 = 18 + 0.5625 Reorder the terms: 0.5625 + -1.5X + X2 = 18 + 0.5625 Combine like terms: 18 + 0.5625 = 18.5625 0.5625 + -1.5X + X2 = 18.5625 Factor a perfect square on the left side: (X + -0.75)(X + -0.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (X + -0.75) equal to 4.308421985 and -4.308421985.Subproblem 1
X + -0.75 = 4.308421985 Simplifying X + -0.75 = 4.308421985 Reorder the terms: -0.75 + X = 4.308421985 Solving -0.75 + X = 4.308421985 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + X = 4.308421985 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = 4.308421985 + 0.75 X = 4.308421985 + 0.75 Combine like terms: 4.308421985 + 0.75 = 5.058421985 X = 5.058421985 Simplifying X = 5.058421985Subproblem 2
X + -0.75 = -4.308421985 Simplifying X + -0.75 = -4.308421985 Reorder the terms: -0.75 + X = -4.308421985 Solving -0.75 + X = -4.308421985 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + X = -4.308421985 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = -4.308421985 + 0.75 X = -4.308421985 + 0.75 Combine like terms: -4.308421985 + 0.75 = -3.558421985 X = -3.558421985 Simplifying X = -3.558421985Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.058421985, -3.558421985}
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