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Simplifying x(9 + 2x) = 120 (9 * x + 2x * x) = 120 (9x + 2x2) = 120 Solving 9x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 9x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60 + 4.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 4.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 4.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 4.5x + x2 = 0 + 60 4.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 4.5x + x2 = 60 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 = 60 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 60 + 5.0625 Combine like terms: 60 + 5.0625 = 65.0625 5.0625 + 4.5x + x2 = 65.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 65.0625 Calculate the square root of the right side: 8.066132902 Break this problem into two subproblems by setting (x + 2.25) equal to 8.066132902 and -8.066132902.Subproblem 1
x + 2.25 = 8.066132902 Simplifying x + 2.25 = 8.066132902 Reorder the terms: 2.25 + x = 8.066132902 Solving 2.25 + x = 8.066132902 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 = 8.066132902 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 8.066132902 + -2.25 x = 8.066132902 + -2.25 Combine like terms: 8.066132902 + -2.25 = 5.816132902 x = 5.816132902 Simplifying x = 5.816132902Subproblem 2
x + 2.25 = -8.066132902 Simplifying x + 2.25 = -8.066132902 Reorder the terms: 2.25 + x = -8.066132902 Solving 2.25 + x = -8.066132902 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 = -8.066132902 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -8.066132902 + -2.25 x = -8.066132902 + -2.25 Combine like terms: -8.066132902 + -2.25 = -10.316132902 x = -10.316132902 Simplifying x = -10.316132902Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.816132902, -10.316132902}
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