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Simplifying y2 + -9y + 6 = 0 Reorder the terms: 6 + -9y + y2 = 0 Solving 6 + -9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + -9y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9y + y2 = 0 + -6 -9y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9y + y2 = -6 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = -6 + 20.25 Reorder the terms: 20.25 + -9y + y2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9y + y2 = 14.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y + -4.5 = 3.774917218 Simplifying y + -4.5 = 3.774917218 Reorder the terms: -4.5 + y = 3.774917218 Solving -4.5 + y = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 3.774917218 + 4.5 y = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 y = 8.274917218 Simplifying y = 8.274917218Subproblem 2
y + -4.5 = -3.774917218 Simplifying y + -4.5 = -3.774917218 Reorder the terms: -4.5 + y = -3.774917218 Solving -4.5 + y = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -3.774917218 + 4.5 y = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 y = 0.725082782 Simplifying y = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.274917218, 0.725082782}
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