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Simplifying 4x2 + 9x = 480 Reorder the terms: 9x + 4x2 = 480 Solving 9x + 4x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 9x + 4x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -120 + 2.25x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 2.25x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 2.25x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 2.25x + x2 = 0 + 120 2.25x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 2.25x + x2 = 120 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 120 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 120 + 1.265625 Combine like terms: 120 + 1.265625 = 121.265625 1.265625 + 2.25x + x2 = 121.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 121.265625 Calculate the square root of the right side: 11.012067245 Break this problem into two subproblems by setting (x + 1.125) equal to 11.012067245 and -11.012067245.Subproblem 1
x + 1.125 = 11.012067245 Simplifying x + 1.125 = 11.012067245 Reorder the terms: 1.125 + x = 11.012067245 Solving 1.125 + x = 11.012067245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 11.012067245 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 11.012067245 + -1.125 x = 11.012067245 + -1.125 Combine like terms: 11.012067245 + -1.125 = 9.887067245 x = 9.887067245 Simplifying x = 9.887067245Subproblem 2
x + 1.125 = -11.012067245 Simplifying x + 1.125 = -11.012067245 Reorder the terms: 1.125 + x = -11.012067245 Solving 1.125 + x = -11.012067245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -11.012067245 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -11.012067245 + -1.125 x = -11.012067245 + -1.125 Combine like terms: -11.012067245 + -1.125 = -12.137067245 x = -12.137067245 Simplifying x = -12.137067245Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.887067245, -12.137067245}
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