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Simplifying 9y2 + -21y + 4 = 0 Reorder the terms: 4 + -21y + 9y2 = 0 Solving 4 + -21y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -2.333333333y + -0.4444444444 + y2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -2.333333333y + y2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -2.333333333y + y2 = 0 + -0.4444444444 -2.333333333y + y2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -2.333333333y + y2 = -0.4444444444 The y term is -2.333333333y. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333y + 1.361111112 + y2 = -0.4444444444 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = -0.4444444444 + 1.361111112 Combine like terms: -0.4444444444 + 1.361111112 = 0.9166666676 1.361111112 + -2.333333333y + y2 = 0.9166666676 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 0.9166666676 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (y + -1.166666667) equal to 0.957427108 and -0.957427108.Subproblem 1
y + -1.166666667 = 0.957427108 Simplifying y + -1.166666667 = 0.957427108 Reorder the terms: -1.166666667 + y = 0.957427108 Solving -1.166666667 + y = 0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = 0.957427108 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 0.957427108 + 1.166666667 y = 0.957427108 + 1.166666667 Combine like terms: 0.957427108 + 1.166666667 = 2.124093775 y = 2.124093775 Simplifying y = 2.124093775Subproblem 2
y + -1.166666667 = -0.957427108 Simplifying y + -1.166666667 = -0.957427108 Reorder the terms: -1.166666667 + y = -0.957427108 Solving -1.166666667 + y = -0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + y = -0.957427108 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -0.957427108 + 1.166666667 y = -0.957427108 + 1.166666667 Combine like terms: -0.957427108 + 1.166666667 = 0.209239559 y = 0.209239559 Simplifying y = 0.209239559Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.124093775, 0.209239559}
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