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Simplifying x(x) + 20x + -80000 = 0 Multiply x * x x2 + 20x + -80000 = 0 Reorder the terms: -80000 + 20x + x2 = 0 Solving -80000 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80000' to each side of the equation. -80000 + 20x + 80000 + x2 = 0 + 80000 Reorder the terms: -80000 + 80000 + 20x + x2 = 0 + 80000 Combine like terms: -80000 + 80000 = 0 0 + 20x + x2 = 0 + 80000 20x + x2 = 0 + 80000 Combine like terms: 0 + 80000 = 80000 20x + x2 = 80000 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 = 80000 + 100 Reorder the terms: 100 + 20x + x2 = 80000 + 100 Combine like terms: 80000 + 100 = 80100 100 + 20x + x2 = 80100 Factor a perfect square on the left side: (x + 10)(x + 10) = 80100 Calculate the square root of the right side: 283.019433962 Break this problem into two subproblems by setting (x + 10) equal to 283.019433962 and -283.019433962.Subproblem 1
x + 10 = 283.019433962 Simplifying x + 10 = 283.019433962 Reorder the terms: 10 + x = 283.019433962 Solving 10 + x = 283.019433962 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 = 283.019433962 + -10 Combine like terms: 10 + -10 = 0 0 + x = 283.019433962 + -10 x = 283.019433962 + -10 Combine like terms: 283.019433962 + -10 = 273.019433962 x = 273.019433962 Simplifying x = 273.019433962Subproblem 2
x + 10 = -283.019433962 Simplifying x + 10 = -283.019433962 Reorder the terms: 10 + x = -283.019433962 Solving 10 + x = -283.019433962 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 = -283.019433962 + -10 Combine like terms: 10 + -10 = 0 0 + x = -283.019433962 + -10 x = -283.019433962 + -10 Combine like terms: -283.019433962 + -10 = -293.019433962 x = -293.019433962 Simplifying x = -293.019433962Solution
The solution to the problem is based on the solutions from the subproblems. x = {273.019433962, -293.019433962}
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