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Simplifying 2x2 + 9x + -216 = 0 Reorder the terms: -216 + 9x + 2x2 = 0 Solving -216 + 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'. -108 + 4.5x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 4.5x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 4.5x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 4.5x + x2 = 0 + 108 4.5x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 4.5x + x2 = 108 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 = 108 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 108 + 5.0625 Combine like terms: 108 + 5.0625 = 113.0625 5.0625 + 4.5x + x2 = 113.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 113.0625 Calculate the square root of the right side: 10.633085159 Break this problem into two subproblems by setting (x + 2.25) equal to 10.633085159 and -10.633085159.Subproblem 1
x + 2.25 = 10.633085159 Simplifying x + 2.25 = 10.633085159 Reorder the terms: 2.25 + x = 10.633085159 Solving 2.25 + x = 10.633085159 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 = 10.633085159 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 10.633085159 + -2.25 x = 10.633085159 + -2.25 Combine like terms: 10.633085159 + -2.25 = 8.383085159 x = 8.383085159 Simplifying x = 8.383085159Subproblem 2
x + 2.25 = -10.633085159 Simplifying x + 2.25 = -10.633085159 Reorder the terms: 2.25 + x = -10.633085159 Solving 2.25 + x = -10.633085159 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 = -10.633085159 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -10.633085159 + -2.25 x = -10.633085159 + -2.25 Combine like terms: -10.633085159 + -2.25 = -12.883085159 x = -12.883085159 Simplifying x = -12.883085159Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.383085159, -12.883085159}
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