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Simplifying 10y + 20 = y2 + 4y Reorder the terms: 20 + 10y = y2 + 4y Reorder the terms: 20 + 10y = 4y + y2 Solving 20 + 10y = 4y + y2 Solving for variable 'y'. Combine like terms: 10y + -4y = 6y 20 + 6y + -1y2 = 4y + y2 + -4y + -1y2 Reorder the terms: 20 + 6y + -1y2 = 4y + -4y + y2 + -1y2 Combine like terms: 4y + -4y = 0 20 + 6y + -1y2 = 0 + y2 + -1y2 20 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 20 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -6y + y2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -6y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + -6y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6y + y2 = 0 + 20 -6y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6y + y2 = 20 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 20 + 9 Reorder the terms: 9 + -6y + y2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + -6y + y2 = 29 Factor a perfect square on the left side: (y + -3)(y + -3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (y + -3) equal to 5.385164807 and -5.385164807.Subproblem 1
y + -3 = 5.385164807 Simplifying y + -3 = 5.385164807 Reorder the terms: -3 + y = 5.385164807 Solving -3 + y = 5.385164807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + y = 5.385164807 + 3 y = 5.385164807 + 3 Combine like terms: 5.385164807 + 3 = 8.385164807 y = 8.385164807 Simplifying y = 8.385164807Subproblem 2
y + -3 = -5.385164807 Simplifying y + -3 = -5.385164807 Reorder the terms: -3 + y = -5.385164807 Solving -3 + y = -5.385164807 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + y = -5.385164807 + 3 y = -5.385164807 + 3 Combine like terms: -5.385164807 + 3 = -2.385164807 y = -2.385164807 Simplifying y = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.385164807, -2.385164807}
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