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Simplifying 21y + -1(y(y + -1)) = 4 Reorder the terms: 21y + -1(y(-1 + y)) = 4 21y + -1((-1 * y + y * y)) = 4 21y + -1((-1y + y2)) = 4 21y + (-1y * -1 + y2 * -1) = 4 21y + (1y + -1y2) = 4 Combine like terms: 21y + 1y = 22y 22y + -1y2 = 4 Solving 22y + -1y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 22y + -1y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 22y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -22y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -22y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -22y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -22y + y2 = 0 + -4 -22y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -22y + y2 = -4 The y term is -22y. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22y + 121 + y2 = -4 + 121 Reorder the terms: 121 + -22y + y2 = -4 + 121 Combine like terms: -4 + 121 = 117 121 + -22y + y2 = 117 Factor a perfect square on the left side: (y + -11)(y + -11) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (y + -11) equal to 10.816653826 and -10.816653826.Subproblem 1
y + -11 = 10.816653826 Simplifying y + -11 = 10.816653826 Reorder the terms: -11 + y = 10.816653826 Solving -11 + y = 10.816653826 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = 10.816653826 + 11 Combine like terms: -11 + 11 = 0 0 + y = 10.816653826 + 11 y = 10.816653826 + 11 Combine like terms: 10.816653826 + 11 = 21.816653826 y = 21.816653826 Simplifying y = 21.816653826Subproblem 2
y + -11 = -10.816653826 Simplifying y + -11 = -10.816653826 Reorder the terms: -11 + y = -10.816653826 Solving -11 + y = -10.816653826 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = -10.816653826 + 11 Combine like terms: -11 + 11 = 0 0 + y = -10.816653826 + 11 y = -10.816653826 + 11 Combine like terms: -10.816653826 + 11 = 0.183346174 y = 0.183346174 Simplifying y = 0.183346174Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.816653826, 0.183346174}
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