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Simplifying 2x2 + 9x + 9 = 180 Reorder the terms: 9 + 9x + 2x2 = 180 Solving 9 + 9x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 9 + -180 + 9x + 2x2 = 180 + -180 Combine like terms: 9 + -180 = -171 -171 + 9x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -171 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -85.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '85.5' to each side of the equation. -85.5 + 4.5x + 85.5 + x2 = 0 + 85.5 Reorder the terms: -85.5 + 85.5 + 4.5x + x2 = 0 + 85.5 Combine like terms: -85.5 + 85.5 = 0.0 0.0 + 4.5x + x2 = 0 + 85.5 4.5x + x2 = 0 + 85.5 Combine like terms: 0 + 85.5 = 85.5 4.5x + x2 = 85.5 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 = 85.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 85.5 + 5.0625 Combine like terms: 85.5 + 5.0625 = 90.5625 5.0625 + 4.5x + x2 = 90.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 90.5625 Calculate the square root of the right side: 9.516433155 Break this problem into two subproblems by setting (x + 2.25) equal to 9.516433155 and -9.516433155.Subproblem 1
x + 2.25 = 9.516433155 Simplifying x + 2.25 = 9.516433155 Reorder the terms: 2.25 + x = 9.516433155 Solving 2.25 + x = 9.516433155 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 = 9.516433155 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 9.516433155 + -2.25 x = 9.516433155 + -2.25 Combine like terms: 9.516433155 + -2.25 = 7.266433155 x = 7.266433155 Simplifying x = 7.266433155Subproblem 2
x + 2.25 = -9.516433155 Simplifying x + 2.25 = -9.516433155 Reorder the terms: 2.25 + x = -9.516433155 Solving 2.25 + x = -9.516433155 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 = -9.516433155 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -9.516433155 + -2.25 x = -9.516433155 + -2.25 Combine like terms: -9.516433155 + -2.25 = -11.766433155 x = -11.766433155 Simplifying x = -11.766433155Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.266433155, -11.766433155}
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