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Simplifying 0 = 2X2 + -9X + -12 Reorder the terms: 0 = -12 + -9X + 2X2 Solving 0 = -12 + -9X + 2X2 Solving for variable 'X'. Combine like terms: 0 + 12 = 12 12 + 9X + -2X2 = -12 + -9X + 2X2 + 12 + 9X + -2X2 Reorder the terms: 12 + 9X + -2X2 = -12 + 12 + -9X + 9X + 2X2 + -2X2 Combine like terms: -12 + 12 = 0 12 + 9X + -2X2 = 0 + -9X + 9X + 2X2 + -2X2 12 + 9X + -2X2 = -9X + 9X + 2X2 + -2X2 Combine like terms: -9X + 9X = 0 12 + 9X + -2X2 = 0 + 2X2 + -2X2 12 + 9X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 12 + 9X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -4.5X + X2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4.5X + 6 + X2 = 0 + 6 Reorder the terms: -6 + 6 + -4.5X + X2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4.5X + X2 = 0 + 6 -4.5X + X2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4.5X + X2 = 6 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 = 6 + 5.0625 Reorder the terms: 5.0625 + -4.5X + X2 = 6 + 5.0625 Combine like terms: 6 + 5.0625 = 11.0625 5.0625 + -4.5X + X2 = 11.0625 Factor a perfect square on the left side: (X + -2.25)(X + -2.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (X + -2.25) equal to 3.326033674 and -3.326033674.Subproblem 1
X + -2.25 = 3.326033674 Simplifying X + -2.25 = 3.326033674 Reorder the terms: -2.25 + X = 3.326033674 Solving -2.25 + X = 3.326033674 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 = 3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = 3.326033674 + 2.25 X = 3.326033674 + 2.25 Combine like terms: 3.326033674 + 2.25 = 5.576033674 X = 5.576033674 Simplifying X = 5.576033674Subproblem 2
X + -2.25 = -3.326033674 Simplifying X + -2.25 = -3.326033674 Reorder the terms: -2.25 + X = -3.326033674 Solving -2.25 + X = -3.326033674 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 = -3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + X = -3.326033674 + 2.25 X = -3.326033674 + 2.25 Combine like terms: -3.326033674 + 2.25 = -1.076033674 X = -1.076033674 Simplifying X = -1.076033674Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.576033674, -1.076033674}
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