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Simplifying x2 + 9x + -480 = 0 Reorder the terms: -480 + 9x + x2 = 0 Solving -480 + 9x + 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 + 9x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 9x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 9x + x2 = 0 + 480 9x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 9x + x2 = 480 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 480 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 480 + 20.25 Combine like terms: 480 + 20.25 = 500.25 20.25 + 9x + x2 = 500.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 500.25 Calculate the square root of the right side: 22.366269246 Break this problem into two subproblems by setting (x + 4.5) equal to 22.366269246 and -22.366269246.Subproblem 1
x + 4.5 = 22.366269246 Simplifying x + 4.5 = 22.366269246 Reorder the terms: 4.5 + x = 22.366269246 Solving 4.5 + x = 22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 22.366269246 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 22.366269246 + -4.5 x = 22.366269246 + -4.5 Combine like terms: 22.366269246 + -4.5 = 17.866269246 x = 17.866269246 Simplifying x = 17.866269246Subproblem 2
x + 4.5 = -22.366269246 Simplifying x + 4.5 = -22.366269246 Reorder the terms: 4.5 + x = -22.366269246 Solving 4.5 + x = -22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -22.366269246 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -22.366269246 + -4.5 x = -22.366269246 + -4.5 Combine like terms: -22.366269246 + -4.5 = -26.866269246 x = -26.866269246 Simplifying x = -26.866269246Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.866269246, -26.866269246}
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