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Simplifying (3y2 + -5y + -7) + (6y2 + -2y + 1) = 0 Reorder the terms: (-7 + -5y + 3y2) + (6y2 + -2y + 1) = 0 Remove parenthesis around (-7 + -5y + 3y2) -7 + -5y + 3y2 + (6y2 + -2y + 1) = 0 Reorder the terms: -7 + -5y + 3y2 + (1 + -2y + 6y2) = 0 Remove parenthesis around (1 + -2y + 6y2) -7 + -5y + 3y2 + 1 + -2y + 6y2 = 0 Reorder the terms: -7 + 1 + -5y + -2y + 3y2 + 6y2 = 0 Combine like terms: -7 + 1 = -6 -6 + -5y + -2y + 3y2 + 6y2 = 0 Combine like terms: -5y + -2y = -7y -6 + -7y + 3y2 + 6y2 = 0 Combine like terms: 3y2 + 6y2 = 9y2 -6 + -7y + 9y2 = 0 Solving -6 + -7y + 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'. -0.6666666667 + -0.7777777778y + y2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.7777777778y + 0.6666666667 + y2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.7777777778y + y2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.7777777778y + y2 = 0 + 0.6666666667 -0.7777777778y + y2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.7777777778y + y2 = 0.6666666667 The y term is -0.7777777778y. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778y + 0.1512345679 + y2 = 0.6666666667 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778y + y2 = 0.6666666667 + 0.1512345679 Combine like terms: 0.6666666667 + 0.1512345679 = 0.8179012346 0.1512345679 + -0.7777777778y + y2 = 0.8179012346 Factor a perfect square on the left side: (y + -0.3888888889)(y + -0.3888888889) = 0.8179012346 Calculate the square root of the right side: 0.904378922 Break this problem into two subproblems by setting (y + -0.3888888889) equal to 0.904378922 and -0.904378922.Subproblem 1
y + -0.3888888889 = 0.904378922 Simplifying y + -0.3888888889 = 0.904378922 Reorder the terms: -0.3888888889 + y = 0.904378922 Solving -0.3888888889 + y = 0.904378922 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + y = 0.904378922 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + y = 0.904378922 + 0.3888888889 y = 0.904378922 + 0.3888888889 Combine like terms: 0.904378922 + 0.3888888889 = 1.2932678109 y = 1.2932678109 Simplifying y = 1.2932678109Subproblem 2
y + -0.3888888889 = -0.904378922 Simplifying y + -0.3888888889 = -0.904378922 Reorder the terms: -0.3888888889 + y = -0.904378922 Solving -0.3888888889 + y = -0.904378922 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + y = -0.904378922 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + y = -0.904378922 + 0.3888888889 y = -0.904378922 + 0.3888888889 Combine like terms: -0.904378922 + 0.3888888889 = -0.5154900331 y = -0.5154900331 Simplifying y = -0.5154900331Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2932678109, -0.5154900331}
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