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Simplifying x2 + 22x + -480 = 0 Reorder the terms: -480 + 22x + x2 = 0 Solving -480 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 22x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 22x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 22x + x2 = 0 + 480 22x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 22x + x2 = 480 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 480 + 121 Reorder the terms: 121 + 22x + x2 = 480 + 121 Combine like terms: 480 + 121 = 601 121 + 22x + x2 = 601 Factor a perfect square on the left side: (x + 11)(x + 11) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (x + 11) equal to 24.515301344 and -24.515301344.Subproblem 1
x + 11 = 24.515301344 Simplifying x + 11 = 24.515301344 Reorder the terms: 11 + x = 24.515301344 Solving 11 + x = 24.515301344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 24.515301344 + -11 Combine like terms: 11 + -11 = 0 0 + x = 24.515301344 + -11 x = 24.515301344 + -11 Combine like terms: 24.515301344 + -11 = 13.515301344 x = 13.515301344 Simplifying x = 13.515301344Subproblem 2
x + 11 = -24.515301344 Simplifying x + 11 = -24.515301344 Reorder the terms: 11 + x = -24.515301344 Solving 11 + x = -24.515301344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -24.515301344 + -11 Combine like terms: 11 + -11 = 0 0 + x = -24.515301344 + -11 x = -24.515301344 + -11 Combine like terms: -24.515301344 + -11 = -35.515301344 x = -35.515301344 Simplifying x = -35.515301344Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.515301344, -35.515301344}
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