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Simplifying 100000000 + -30000y + y2 = 0 Solving 100000000 + -30000y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-100000000' to each side of the equation. 100000000 + -30000y + -100000000 + y2 = 0 + -100000000 Reorder the terms: 100000000 + -100000000 + -30000y + y2 = 0 + -100000000 Combine like terms: 100000000 + -100000000 = 0 0 + -30000y + y2 = 0 + -100000000 -30000y + y2 = 0 + -100000000 Combine like terms: 0 + -100000000 = -100000000 -30000y + y2 = -100000000 The y term is -30000y. Take half its coefficient (-15000). Square it (225000000) and add it to both sides. Add '225000000' to each side of the equation. -30000y + 225000000 + y2 = -100000000 + 225000000 Reorder the terms: 225000000 + -30000y + y2 = -100000000 + 225000000 Combine like terms: -100000000 + 225000000 = 125000000 225000000 + -30000y + y2 = 125000000 Factor a perfect square on the left side: (y + -15000)(y + -15000) = 125000000 Calculate the square root of the right side: 11180.339887499 Break this problem into two subproblems by setting (y + -15000) equal to 11180.339887499 and -11180.339887499.Subproblem 1
y + -15000 = 11180.339887499 Simplifying y + -15000 = 11180.339887499 Reorder the terms: -15000 + y = 11180.339887499 Solving -15000 + y = 11180.339887499 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + y = 11180.339887499 + 15000 Combine like terms: -15000 + 15000 = 0 0 + y = 11180.339887499 + 15000 y = 11180.339887499 + 15000 Combine like terms: 11180.339887499 + 15000 = 26180.339887499 y = 26180.339887499 Simplifying y = 26180.339887499Subproblem 2
y + -15000 = -11180.339887499 Simplifying y + -15000 = -11180.339887499 Reorder the terms: -15000 + y = -11180.339887499 Solving -15000 + y = -11180.339887499 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + y = -11180.339887499 + 15000 Combine like terms: -15000 + 15000 = 0 0 + y = -11180.339887499 + 15000 y = -11180.339887499 + 15000 Combine like terms: -11180.339887499 + 15000 = 3819.660112501 y = 3819.660112501 Simplifying y = 3819.660112501Solution
The solution to the problem is based on the solutions from the subproblems. y = {26180.339887499, 3819.660112501}
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