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Simplifying 9y2 + -14y + 1 = 0 Reorder the terms: 1 + -14y + 9y2 = 0 Solving 1 + -14y + 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'. 0.1111111111 + -1.555555556y + y2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -1.555555556y + -0.1111111111 + y2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -1.555555556y + y2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -1.555555556y + y2 = 0 + -0.1111111111 -1.555555556y + y2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -1.555555556y + y2 = -0.1111111111 The y term is -1.555555556y. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556y + 0.6049382720 + y2 = -0.1111111111 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556y + y2 = -0.1111111111 + 0.6049382720 Combine like terms: -0.1111111111 + 0.6049382720 = 0.4938271609 0.6049382720 + -1.555555556y + y2 = 0.4938271609 Factor a perfect square on the left side: (y + -0.777777778)(y + -0.777777778) = 0.4938271609 Calculate the square root of the right side: 0.702728369 Break this problem into two subproblems by setting (y + -0.777777778) equal to 0.702728369 and -0.702728369.Subproblem 1
y + -0.777777778 = 0.702728369 Simplifying y + -0.777777778 = 0.702728369 Reorder the terms: -0.777777778 + y = 0.702728369 Solving -0.777777778 + y = 0.702728369 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + y = 0.702728369 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + y = 0.702728369 + 0.777777778 y = 0.702728369 + 0.777777778 Combine like terms: 0.702728369 + 0.777777778 = 1.480506147 y = 1.480506147 Simplifying y = 1.480506147Subproblem 2
y + -0.777777778 = -0.702728369 Simplifying y + -0.777777778 = -0.702728369 Reorder the terms: -0.777777778 + y = -0.702728369 Solving -0.777777778 + y = -0.702728369 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + y = -0.702728369 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + y = -0.702728369 + 0.777777778 y = -0.702728369 + 0.777777778 Combine like terms: -0.702728369 + 0.777777778 = 0.075049409 y = 0.075049409 Simplifying y = 0.075049409Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.480506147, 0.075049409}
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