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Simplifying 2x2 + 9x = 240 Reorder the terms: 9x + 2x2 = 240 Solving 9x + 2x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 9x + 2x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -120 + 4.5x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 4.5x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 4.5x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 4.5x + x2 = 0 + 120 4.5x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 4.5x + x2 = 120 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 = 120 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 120 + 5.0625 Combine like terms: 120 + 5.0625 = 125.0625 5.0625 + 4.5x + x2 = 125.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 125.0625 Calculate the square root of the right side: 11.183134623 Break this problem into two subproblems by setting (x + 2.25) equal to 11.183134623 and -11.183134623.Subproblem 1
x + 2.25 = 11.183134623 Simplifying x + 2.25 = 11.183134623 Reorder the terms: 2.25 + x = 11.183134623 Solving 2.25 + x = 11.183134623 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 = 11.183134623 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 11.183134623 + -2.25 x = 11.183134623 + -2.25 Combine like terms: 11.183134623 + -2.25 = 8.933134623 x = 8.933134623 Simplifying x = 8.933134623Subproblem 2
x + 2.25 = -11.183134623 Simplifying x + 2.25 = -11.183134623 Reorder the terms: 2.25 + x = -11.183134623 Solving 2.25 + x = -11.183134623 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 = -11.183134623 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -11.183134623 + -2.25 x = -11.183134623 + -2.25 Combine like terms: -11.183134623 + -2.25 = -13.433134623 x = -13.433134623 Simplifying x = -13.433134623Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.933134623, -13.433134623}
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