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Simplifying -1y2 + 9y + 6 = 0 Reorder the terms: 6 + 9y + -1y2 = 0 Solving 6 + 9y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -9y + y2 = 0 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 = 26.25 20.25 + -9y + y2 = 26.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + -4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + -4.5 = 5.123475383 Simplifying y + -4.5 = 5.123475383 Reorder the terms: -4.5 + y = 5.123475383 Solving -4.5 + y = 5.123475383 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 = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 5.123475383 + 4.5 y = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 y = 9.623475383 Simplifying y = 9.623475383Subproblem 2
y + -4.5 = -5.123475383 Simplifying y + -4.5 = -5.123475383 Reorder the terms: -4.5 + y = -5.123475383 Solving -4.5 + y = -5.123475383 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 = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -5.123475383 + 4.5 y = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 y = -0.623475383 Simplifying y = -0.623475383Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.623475383, -0.623475383}
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