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Simplifying 2x2 + 81x + -960 = 0 Reorder the terms: -960 + 81x + 2x2 = 0 Solving -960 + 81x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -480 + 40.5x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 40.5x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 40.5x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 40.5x + x2 = 0 + 480 40.5x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 40.5x + x2 = 480 The x term is 40.5x. Take half its coefficient (20.25). Square it (410.0625) and add it to both sides. Add '410.0625' to each side of the equation. 40.5x + 410.0625 + x2 = 480 + 410.0625 Reorder the terms: 410.0625 + 40.5x + x2 = 480 + 410.0625 Combine like terms: 480 + 410.0625 = 890.0625 410.0625 + 40.5x + x2 = 890.0625 Factor a perfect square on the left side: (x + 20.25)(x + 20.25) = 890.0625 Calculate the square root of the right side: 29.833915264 Break this problem into two subproblems by setting (x + 20.25) equal to 29.833915264 and -29.833915264.Subproblem 1
x + 20.25 = 29.833915264 Simplifying x + 20.25 = 29.833915264 Reorder the terms: 20.25 + x = 29.833915264 Solving 20.25 + x = 29.833915264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.25' to each side of the equation. 20.25 + -20.25 + x = 29.833915264 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + x = 29.833915264 + -20.25 x = 29.833915264 + -20.25 Combine like terms: 29.833915264 + -20.25 = 9.583915264 x = 9.583915264 Simplifying x = 9.583915264Subproblem 2
x + 20.25 = -29.833915264 Simplifying x + 20.25 = -29.833915264 Reorder the terms: 20.25 + x = -29.833915264 Solving 20.25 + x = -29.833915264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.25' to each side of the equation. 20.25 + -20.25 + x = -29.833915264 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + x = -29.833915264 + -20.25 x = -29.833915264 + -20.25 Combine like terms: -29.833915264 + -20.25 = -50.083915264 x = -50.083915264 Simplifying x = -50.083915264Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.583915264, -50.083915264}
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