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Simplifying y2 + -40y + -3 = 0 Reorder the terms: -3 + -40y + y2 = 0 Solving -3 + -40y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -40y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -40y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -40y + y2 = 0 + 3 -40y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -40y + y2 = 3 The y term is -40y. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40y + 400 + y2 = 3 + 400 Reorder the terms: 400 + -40y + y2 = 3 + 400 Combine like terms: 3 + 400 = 403 400 + -40y + y2 = 403 Factor a perfect square on the left side: (y + -20)(y + -20) = 403 Calculate the square root of the right side: 20.0748599 Break this problem into two subproblems by setting (y + -20) equal to 20.0748599 and -20.0748599.Subproblem 1
y + -20 = 20.0748599 Simplifying y + -20 = 20.0748599 Reorder the terms: -20 + y = 20.0748599 Solving -20 + y = 20.0748599 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = 20.0748599 + 20 Combine like terms: -20 + 20 = 0 0 + y = 20.0748599 + 20 y = 20.0748599 + 20 Combine like terms: 20.0748599 + 20 = 40.0748599 y = 40.0748599 Simplifying y = 40.0748599Subproblem 2
y + -20 = -20.0748599 Simplifying y + -20 = -20.0748599 Reorder the terms: -20 + y = -20.0748599 Solving -20 + y = -20.0748599 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = -20.0748599 + 20 Combine like terms: -20 + 20 = 0 0 + y = -20.0748599 + 20 y = -20.0748599 + 20 Combine like terms: -20.0748599 + 20 = -0.0748599 y = -0.0748599 Simplifying y = -0.0748599Solution
The solution to the problem is based on the solutions from the subproblems. y = {40.0748599, -0.0748599}
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