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Simplifying 2x2 + 9x + 9 = 66 Reorder the terms: 9 + 9x + 2x2 = 66 Solving 9 + 9x + 2x2 = 66 Solving for variable 'x'. Reorder the terms: 9 + -66 + 9x + 2x2 = 66 + -66 Combine like terms: 9 + -66 = -57 -57 + 9x + 2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -57 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 4.5x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 4.5x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 4.5x + x2 = 0 + 28.5 4.5x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 4.5x + x2 = 28.5 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 = 28.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 28.5 + 5.0625 Combine like terms: 28.5 + 5.0625 = 33.5625 5.0625 + 4.5x + x2 = 33.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 33.5625 Calculate the square root of the right side: 5.793315113 Break this problem into two subproblems by setting (x + 2.25) equal to 5.793315113 and -5.793315113.Subproblem 1
x + 2.25 = 5.793315113 Simplifying x + 2.25 = 5.793315113 Reorder the terms: 2.25 + x = 5.793315113 Solving 2.25 + x = 5.793315113 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 = 5.793315113 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.793315113 + -2.25 x = 5.793315113 + -2.25 Combine like terms: 5.793315113 + -2.25 = 3.543315113 x = 3.543315113 Simplifying x = 3.543315113Subproblem 2
x + 2.25 = -5.793315113 Simplifying x + 2.25 = -5.793315113 Reorder the terms: 2.25 + x = -5.793315113 Solving 2.25 + x = -5.793315113 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 = -5.793315113 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.793315113 + -2.25 x = -5.793315113 + -2.25 Combine like terms: -5.793315113 + -2.25 = -8.043315113 x = -8.043315113 Simplifying x = -8.043315113Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.543315113, -8.043315113}
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