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Simplifying 21y2 + -125y = -35 Reorder the terms: -125y + 21y2 = -35 Solving -125y + 21y2 = -35 Solving for variable 'y'. Reorder the terms: 35 + -125y + 21y2 = -35 + 35 Combine like terms: -35 + 35 = 0 35 + -125y + 21y2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 1.666666667 + -5.952380952y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -5.952380952y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -5.952380952y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -5.952380952y + y2 = 0 + -1.666666667 -5.952380952y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -5.952380952y + y2 = -1.666666667 The y term is -5.952380952y. Take half its coefficient (-2.976190476). Square it (8.857709749) and add it to both sides. Add '8.857709749' to each side of the equation. -5.952380952y + 8.857709749 + y2 = -1.666666667 + 8.857709749 Reorder the terms: 8.857709749 + -5.952380952y + y2 = -1.666666667 + 8.857709749 Combine like terms: -1.666666667 + 8.857709749 = 7.191043082 8.857709749 + -5.952380952y + y2 = 7.191043082 Factor a perfect square on the left side: (y + -2.976190476)(y + -2.976190476) = 7.191043082 Calculate the square root of the right side: 2.68161203 Break this problem into two subproblems by setting (y + -2.976190476) equal to 2.68161203 and -2.68161203.Subproblem 1
y + -2.976190476 = 2.68161203 Simplifying y + -2.976190476 = 2.68161203 Reorder the terms: -2.976190476 + y = 2.68161203 Solving -2.976190476 + y = 2.68161203 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.976190476' to each side of the equation. -2.976190476 + 2.976190476 + y = 2.68161203 + 2.976190476 Combine like terms: -2.976190476 + 2.976190476 = 0.000000000 0.000000000 + y = 2.68161203 + 2.976190476 y = 2.68161203 + 2.976190476 Combine like terms: 2.68161203 + 2.976190476 = 5.657802506 y = 5.657802506 Simplifying y = 5.657802506Subproblem 2
y + -2.976190476 = -2.68161203 Simplifying y + -2.976190476 = -2.68161203 Reorder the terms: -2.976190476 + y = -2.68161203 Solving -2.976190476 + y = -2.68161203 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.976190476' to each side of the equation. -2.976190476 + 2.976190476 + y = -2.68161203 + 2.976190476 Combine like terms: -2.976190476 + 2.976190476 = 0.000000000 0.000000000 + y = -2.68161203 + 2.976190476 y = -2.68161203 + 2.976190476 Combine like terms: -2.68161203 + 2.976190476 = 0.294578446 y = 0.294578446 Simplifying y = 0.294578446Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.657802506, 0.294578446}
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