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Simplifying (20000 + -1x)(10000 + -1x) = 100000000 Multiply (20000 + -1x) * (10000 + -1x) (20000(10000 + -1x) + -1x * (10000 + -1x)) = 100000000 ((10000 * 20000 + -1x * 20000) + -1x * (10000 + -1x)) = 100000000 ((200000000 + -20000x) + -1x * (10000 + -1x)) = 100000000 (200000000 + -20000x + (10000 * -1x + -1x * -1x)) = 100000000 (200000000 + -20000x + (-10000x + 1x2)) = 100000000 Combine like terms: -20000x + -10000x = -30000x (200000000 + -30000x + 1x2) = 100000000 Solving 200000000 + -30000x + 1x2 = 100000000 Solving for variable 'x'. Reorder the terms: 200000000 + -100000000 + -30000x + 1x2 = 100000000 + -100000000 Combine like terms: 200000000 + -100000000 = 100000000 100000000 + -30000x + 1x2 = 100000000 + -100000000 Combine like terms: 100000000 + -100000000 = 0 100000000 + -30000x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100000000' to each side of the equation. 100000000 + -30000x + -100000000 + x2 = 0 + -100000000 Reorder the terms: 100000000 + -100000000 + -30000x + x2 = 0 + -100000000 Combine like terms: 100000000 + -100000000 = 0 0 + -30000x + x2 = 0 + -100000000 -30000x + x2 = 0 + -100000000 Combine like terms: 0 + -100000000 = -100000000 -30000x + x2 = -100000000 The x term is -30000x. Take half its coefficient (-15000). Square it (225000000) and add it to both sides. Add '225000000' to each side of the equation. -30000x + 225000000 + x2 = -100000000 + 225000000 Reorder the terms: 225000000 + -30000x + x2 = -100000000 + 225000000 Combine like terms: -100000000 + 225000000 = 125000000 225000000 + -30000x + x2 = 125000000 Factor a perfect square on the left side: (x + -15000)(x + -15000) = 125000000 Calculate the square root of the right side: 11180.339887499 Break this problem into two subproblems by setting (x + -15000) equal to 11180.339887499 and -11180.339887499.Subproblem 1
x + -15000 = 11180.339887499 Simplifying x + -15000 = 11180.339887499 Reorder the terms: -15000 + x = 11180.339887499 Solving -15000 + x = 11180.339887499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + x = 11180.339887499 + 15000 Combine like terms: -15000 + 15000 = 0 0 + x = 11180.339887499 + 15000 x = 11180.339887499 + 15000 Combine like terms: 11180.339887499 + 15000 = 26180.339887499 x = 26180.339887499 Simplifying x = 26180.339887499Subproblem 2
x + -15000 = -11180.339887499 Simplifying x + -15000 = -11180.339887499 Reorder the terms: -15000 + x = -11180.339887499 Solving -15000 + x = -11180.339887499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + x = -11180.339887499 + 15000 Combine like terms: -15000 + 15000 = 0 0 + x = -11180.339887499 + 15000 x = -11180.339887499 + 15000 Combine like terms: -11180.339887499 + 15000 = 3819.660112501 x = 3819.660112501 Simplifying x = 3819.660112501Solution
The solution to the problem is based on the solutions from the subproblems. x = {26180.339887499, 3819.660112501}
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