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Simplifying 2x2 + 9x = 440 Reorder the terms: 9x + 2x2 = 440 Solving 9x + 2x2 = 440 Solving for variable 'x'. Reorder the terms: -440 + 9x + 2x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -220 + 4.5x + x2 = 0 Move the constant term to the right: Add '220' to each side of the equation. -220 + 4.5x + 220 + x2 = 0 + 220 Reorder the terms: -220 + 220 + 4.5x + x2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + 4.5x + x2 = 0 + 220 4.5x + x2 = 0 + 220 Combine like terms: 0 + 220 = 220 4.5x + x2 = 220 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 = 220 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 220 + 5.0625 Combine like terms: 220 + 5.0625 = 225.0625 5.0625 + 4.5x + x2 = 225.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 225.0625 Calculate the square root of the right side: 15.002083189 Break this problem into two subproblems by setting (x + 2.25) equal to 15.002083189 and -15.002083189.Subproblem 1
x + 2.25 = 15.002083189 Simplifying x + 2.25 = 15.002083189 Reorder the terms: 2.25 + x = 15.002083189 Solving 2.25 + x = 15.002083189 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 = 15.002083189 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 15.002083189 + -2.25 x = 15.002083189 + -2.25 Combine like terms: 15.002083189 + -2.25 = 12.752083189 x = 12.752083189 Simplifying x = 12.752083189Subproblem 2
x + 2.25 = -15.002083189 Simplifying x + 2.25 = -15.002083189 Reorder the terms: 2.25 + x = -15.002083189 Solving 2.25 + x = -15.002083189 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 = -15.002083189 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -15.002083189 + -2.25 x = -15.002083189 + -2.25 Combine like terms: -15.002083189 + -2.25 = -17.252083189 x = -17.252083189 Simplifying x = -17.252083189Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.752083189, -17.252083189}
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