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Simplifying -9y2 + 21y + 26 = 0 Reorder the terms: 26 + 21y + -9y2 = 0 Solving 26 + 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'. -2.888888889 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + -2.333333333y + 2.888888889 + y2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + -2.333333333y + y2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + -2.333333333y + y2 = 0 + 2.888888889 -2.333333333y + y2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 -2.333333333y + y2 = 2.888888889 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 = 2.888888889 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = 2.888888889 + 1.361111112 Combine like terms: 2.888888889 + 1.361111112 = 4.250000001 1.361111112 + -2.333333333y + y2 = 4.250000001 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 4.250000001 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y + -1.166666667) equal to 2.061552813 and -2.061552813.Subproblem 1
y + -1.166666667 = 2.061552813 Simplifying y + -1.166666667 = 2.061552813 Reorder the terms: -1.166666667 + y = 2.061552813 Solving -1.166666667 + y = 2.061552813 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 = 2.061552813 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 2.061552813 + 1.166666667 y = 2.061552813 + 1.166666667 Combine like terms: 2.061552813 + 1.166666667 = 3.22821948 y = 3.22821948 Simplifying y = 3.22821948Subproblem 2
y + -1.166666667 = -2.061552813 Simplifying y + -1.166666667 = -2.061552813 Reorder the terms: -1.166666667 + y = -2.061552813 Solving -1.166666667 + y = -2.061552813 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 = -2.061552813 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -2.061552813 + 1.166666667 y = -2.061552813 + 1.166666667 Combine like terms: -2.061552813 + 1.166666667 = -0.894886146 y = -0.894886146 Simplifying y = -0.894886146Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.22821948, -0.894886146}
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