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Simplifying x2 + 20x + -48000 = 0 Reorder the terms: -48000 + 20x + x2 = 0 Solving -48000 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48000' to each side of the equation. -48000 + 20x + 48000 + x2 = 0 + 48000 Reorder the terms: -48000 + 48000 + 20x + x2 = 0 + 48000 Combine like terms: -48000 + 48000 = 0 0 + 20x + x2 = 0 + 48000 20x + x2 = 0 + 48000 Combine like terms: 0 + 48000 = 48000 20x + x2 = 48000 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 = 48000 + 100 Reorder the terms: 100 + 20x + x2 = 48000 + 100 Combine like terms: 48000 + 100 = 48100 100 + 20x + x2 = 48100 Factor a perfect square on the left side: (x + 10)(x + 10) = 48100 Calculate the square root of the right side: 219.317121995 Break this problem into two subproblems by setting (x + 10) equal to 219.317121995 and -219.317121995.Subproblem 1
x + 10 = 219.317121995 Simplifying x + 10 = 219.317121995 Reorder the terms: 10 + x = 219.317121995 Solving 10 + x = 219.317121995 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 = 219.317121995 + -10 Combine like terms: 10 + -10 = 0 0 + x = 219.317121995 + -10 x = 219.317121995 + -10 Combine like terms: 219.317121995 + -10 = 209.317121995 x = 209.317121995 Simplifying x = 209.317121995Subproblem 2
x + 10 = -219.317121995 Simplifying x + 10 = -219.317121995 Reorder the terms: 10 + x = -219.317121995 Solving 10 + x = -219.317121995 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 = -219.317121995 + -10 Combine like terms: 10 + -10 = 0 0 + x = -219.317121995 + -10 x = -219.317121995 + -10 Combine like terms: -219.317121995 + -10 = -229.317121995 x = -229.317121995 Simplifying x = -229.317121995Solution
The solution to the problem is based on the solutions from the subproblems. x = {209.317121995, -229.317121995}
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