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Simplifying y2 + 1000y + -60000000 = 0 Reorder the terms: -60000000 + 1000y + y2 = 0 Solving -60000000 + 1000y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '60000000' to each side of the equation. -60000000 + 1000y + 60000000 + y2 = 0 + 60000000 Reorder the terms: -60000000 + 60000000 + 1000y + y2 = 0 + 60000000 Combine like terms: -60000000 + 60000000 = 0 0 + 1000y + y2 = 0 + 60000000 1000y + y2 = 0 + 60000000 Combine like terms: 0 + 60000000 = 60000000 1000y + y2 = 60000000 The y term is 1000y. Take half its coefficient (500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. 1000y + 250000 + y2 = 60000000 + 250000 Reorder the terms: 250000 + 1000y + y2 = 60000000 + 250000 Combine like terms: 60000000 + 250000 = 60250000 250000 + 1000y + y2 = 60250000 Factor a perfect square on the left side: (y + 500)(y + 500) = 60250000 Calculate the square root of the right side: 7762.08734813 Break this problem into two subproblems by setting (y + 500) equal to 7762.08734813 and -7762.08734813.Subproblem 1
y + 500 = 7762.08734813 Simplifying y + 500 = 7762.08734813 Reorder the terms: 500 + y = 7762.08734813 Solving 500 + y = 7762.08734813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + y = 7762.08734813 + -500 Combine like terms: 500 + -500 = 0 0 + y = 7762.08734813 + -500 y = 7762.08734813 + -500 Combine like terms: 7762.08734813 + -500 = 7262.08734813 y = 7262.08734813 Simplifying y = 7262.08734813Subproblem 2
y + 500 = -7762.08734813 Simplifying y + 500 = -7762.08734813 Reorder the terms: 500 + y = -7762.08734813 Solving 500 + y = -7762.08734813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + y = -7762.08734813 + -500 Combine like terms: 500 + -500 = 0 0 + y = -7762.08734813 + -500 y = -7762.08734813 + -500 Combine like terms: -7762.08734813 + -500 = -8262.08734813 y = -8262.08734813 Simplifying y = -8262.08734813Solution
The solution to the problem is based on the solutions from the subproblems. y = {7262.08734813, -8262.08734813}
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