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Simplifying (x)(2x + 9) = 320 Reorder the terms: x(9 + 2x) = 320 (9 * x + 2x * x) = 320 (9x + 2x2) = 320 Solving 9x + 2x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + 9x + 2x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -160 + 4.5x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 4.5x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 4.5x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 4.5x + x2 = 0 + 160 4.5x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 4.5x + x2 = 160 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 = 160 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 160 + 5.0625 Combine like terms: 160 + 5.0625 = 165.0625 5.0625 + 4.5x + x2 = 165.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 165.0625 Calculate the square root of the right side: 12.847665158 Break this problem into two subproblems by setting (x + 2.25) equal to 12.847665158 and -12.847665158.Subproblem 1
x + 2.25 = 12.847665158 Simplifying x + 2.25 = 12.847665158 Reorder the terms: 2.25 + x = 12.847665158 Solving 2.25 + x = 12.847665158 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 = 12.847665158 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 12.847665158 + -2.25 x = 12.847665158 + -2.25 Combine like terms: 12.847665158 + -2.25 = 10.597665158 x = 10.597665158 Simplifying x = 10.597665158Subproblem 2
x + 2.25 = -12.847665158 Simplifying x + 2.25 = -12.847665158 Reorder the terms: 2.25 + x = -12.847665158 Solving 2.25 + x = -12.847665158 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 = -12.847665158 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -12.847665158 + -2.25 x = -12.847665158 + -2.25 Combine like terms: -12.847665158 + -2.25 = -15.097665158 x = -15.097665158 Simplifying x = -15.097665158Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.597665158, -15.097665158}
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