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Simplifying x2 + 20x + -480 = 0 Reorder the terms: -480 + 20x + x2 = 0 Solving -480 + 20x + 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 + 20x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 20x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 20x + x2 = 0 + 480 20x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 20x + x2 = 480 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 480 + 100 Reorder the terms: 100 + 20x + x2 = 480 + 100 Combine like terms: 480 + 100 = 580 100 + 20x + x2 = 580 Factor a perfect square on the left side: (x + 10)(x + 10) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (x + 10) equal to 24.083189158 and -24.083189158.Subproblem 1
x + 10 = 24.083189158 Simplifying x + 10 = 24.083189158 Reorder the terms: 10 + x = 24.083189158 Solving 10 + x = 24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 24.083189158 + -10 Combine like terms: 10 + -10 = 0 0 + x = 24.083189158 + -10 x = 24.083189158 + -10 Combine like terms: 24.083189158 + -10 = 14.083189158 x = 14.083189158 Simplifying x = 14.083189158Subproblem 2
x + 10 = -24.083189158 Simplifying x + 10 = -24.083189158 Reorder the terms: 10 + x = -24.083189158 Solving 10 + x = -24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -24.083189158 + -10 Combine like terms: 10 + -10 = 0 0 + x = -24.083189158 + -10 x = -24.083189158 + -10 Combine like terms: -24.083189158 + -10 = -34.083189158 x = -34.083189158 Simplifying x = -34.083189158Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.083189158, -34.083189158}
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