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Simplifying (-6y2) + -9y = -1 Reorder the terms: -9y + (-6y2) = -1 Solving -9y + (-6y2) = -1 Solving for variable 'y'. Reorder the terms: 1 + -9y + (-6y2) = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -9y + (-6y2) = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + 1.5y + y2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 1.5y + 0.1666666667 + y2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 1.5y + y2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 1.5y + y2 = 0 + 0.1666666667 1.5y + y2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 1.5y + y2 = 0.1666666667 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = 0.1666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = 0.1666666667 + 0.5625 Combine like terms: 0.1666666667 + 0.5625 = 0.7291666667 0.5625 + 1.5y + y2 = 0.7291666667 Factor a perfect square on the left side: ((y) + 0.75)((y) + 0.75) = 0.7291666667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting ((y) + 0.75) equal to 0.853912564 and -0.853912564.Subproblem 1
(y) + 0.75 = 0.853912564 Simplifying (y) + 0.75 = 0.853912564 y + 0.75 = 0.853912564 Reorder the terms: 0.75 + y = 0.853912564 Solving 0.75 + y = 0.853912564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 0.853912564 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 0.853912564 + -0.75 y = 0.853912564 + -0.75 Combine like terms: 0.853912564 + -0.75 = 0.103912564 y = 0.103912564 Simplifying y = 0.103912564Subproblem 2
(y) + 0.75 = -0.853912564 Simplifying (y) + 0.75 = -0.853912564 y + 0.75 = -0.853912564 Reorder the terms: 0.75 + y = -0.853912564 Solving 0.75 + y = -0.853912564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -0.853912564 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -0.853912564 + -0.75 y = -0.853912564 + -0.75 Combine like terms: -0.853912564 + -0.75 = -1.603912564 y = -1.603912564 Simplifying y = -1.603912564Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.103912564, -1.603912564}
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