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Simplifying 16X2 + 72X + -81 = 0 Reorder the terms: -81 + 72X + 16X2 = 0 Solving -81 + 72X + 16X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.0625 + 4.5X + X2 = 0 Move the constant term to the right: Add '5.0625' to each side of the equation. -5.0625 + 4.5X + 5.0625 + X2 = 0 + 5.0625 Reorder the terms: -5.0625 + 5.0625 + 4.5X + X2 = 0 + 5.0625 Combine like terms: -5.0625 + 5.0625 = 0.0000 0.0000 + 4.5X + X2 = 0 + 5.0625 4.5X + X2 = 0 + 5.0625 Combine like terms: 0 + 5.0625 = 5.0625 4.5X + X2 = 5.0625 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 = 5.0625 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = 5.0625 + 5.0625 Combine like terms: 5.0625 + 5.0625 = 10.125 5.0625 + 4.5X + X2 = 10.125 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = 10.125 Calculate the square root of the right side: 3.181980515 Break this problem into two subproblems by setting (X + 2.25) equal to 3.181980515 and -3.181980515.Subproblem 1
X + 2.25 = 3.181980515 Simplifying X + 2.25 = 3.181980515 Reorder the terms: 2.25 + X = 3.181980515 Solving 2.25 + X = 3.181980515 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 = 3.181980515 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = 3.181980515 + -2.25 X = 3.181980515 + -2.25 Combine like terms: 3.181980515 + -2.25 = 0.931980515 X = 0.931980515 Simplifying X = 0.931980515Subproblem 2
X + 2.25 = -3.181980515 Simplifying X + 2.25 = -3.181980515 Reorder the terms: 2.25 + X = -3.181980515 Solving 2.25 + X = -3.181980515 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 = -3.181980515 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = -3.181980515 + -2.25 X = -3.181980515 + -2.25 Combine like terms: -3.181980515 + -2.25 = -5.431980515 X = -5.431980515 Simplifying X = -5.431980515Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.931980515, -5.431980515}
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