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Simplifying (6y2 + -6y + -1) + (3y2 + 2y + -5) + -1(-2y2 + 8y + 7) = 0 Reorder the terms: (-1 + -6y + 6y2) + (3y2 + 2y + -5) + -1(-2y2 + 8y + 7) = 0 Remove parenthesis around (-1 + -6y + 6y2) -1 + -6y + 6y2 + (3y2 + 2y + -5) + -1(-2y2 + 8y + 7) = 0 Reorder the terms: -1 + -6y + 6y2 + (-5 + 2y + 3y2) + -1(-2y2 + 8y + 7) = 0 Remove parenthesis around (-5 + 2y + 3y2) -1 + -6y + 6y2 + -5 + 2y + 3y2 + -1(-2y2 + 8y + 7) = 0 Reorder the terms: -1 + -6y + 6y2 + -5 + 2y + 3y2 + -1(7 + 8y + -2y2) = 0 -1 + -6y + 6y2 + -5 + 2y + 3y2 + (7 * -1 + 8y * -1 + -2y2 * -1) = 0 -1 + -6y + 6y2 + -5 + 2y + 3y2 + (-7 + -8y + 2y2) = 0 Reorder the terms: -1 + -5 + -7 + -6y + 2y + -8y + 6y2 + 3y2 + 2y2 = 0 Combine like terms: -1 + -5 = -6 -6 + -7 + -6y + 2y + -8y + 6y2 + 3y2 + 2y2 = 0 Combine like terms: -6 + -7 = -13 -13 + -6y + 2y + -8y + 6y2 + 3y2 + 2y2 = 0 Combine like terms: -6y + 2y = -4y -13 + -4y + -8y + 6y2 + 3y2 + 2y2 = 0 Combine like terms: -4y + -8y = -12y -13 + -12y + 6y2 + 3y2 + 2y2 = 0 Combine like terms: 6y2 + 3y2 = 9y2 -13 + -12y + 9y2 + 2y2 = 0 Combine like terms: 9y2 + 2y2 = 11y2 -13 + -12y + 11y2 = 0 Solving -13 + -12y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.181818182 + -1.090909091y + y2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -1.090909091y + 1.181818182 + y2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -1.090909091y + y2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -1.090909091y + y2 = 0 + 1.181818182 -1.090909091y + y2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -1.090909091y + y2 = 1.181818182 The y term is -1.090909091y. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091y + 0.2975206612 + y2 = 1.181818182 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091y + y2 = 1.181818182 + 0.2975206612 Combine like terms: 1.181818182 + 0.2975206612 = 1.4793388432 0.2975206612 + -1.090909091y + y2 = 1.4793388432 Factor a perfect square on the left side: (y + -0.5454545455)(y + -0.5454545455) = 1.4793388432 Calculate the square root of the right side: 1.216280742 Break this problem into two subproblems by setting (y + -0.5454545455) equal to 1.216280742 and -1.216280742.Subproblem 1
y + -0.5454545455 = 1.216280742 Simplifying y + -0.5454545455 = 1.216280742 Reorder the terms: -0.5454545455 + y = 1.216280742 Solving -0.5454545455 + y = 1.216280742 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = 1.216280742 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = 1.216280742 + 0.5454545455 y = 1.216280742 + 0.5454545455 Combine like terms: 1.216280742 + 0.5454545455 = 1.7617352875 y = 1.7617352875 Simplifying y = 1.7617352875Subproblem 2
y + -0.5454545455 = -1.216280742 Simplifying y + -0.5454545455 = -1.216280742 Reorder the terms: -0.5454545455 + y = -1.216280742 Solving -0.5454545455 + y = -1.216280742 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = -1.216280742 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = -1.216280742 + 0.5454545455 y = -1.216280742 + 0.5454545455 Combine like terms: -1.216280742 + 0.5454545455 = -0.6708261965 y = -0.6708261965 Simplifying y = -0.6708261965Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.7617352875, -0.6708261965}
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