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Simplifying 11y2 + -12y + -4 = 0 Reorder the terms: -4 + -12y + 11y2 = 0 Solving -4 + -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'. -0.3636363636 + -1.090909091y + y2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -1.090909091y + 0.3636363636 + y2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -1.090909091y + y2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -1.090909091y + y2 = 0 + 0.3636363636 -1.090909091y + y2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -1.090909091y + y2 = 0.3636363636 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 = 0.3636363636 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091y + y2 = 0.3636363636 + 0.2975206612 Combine like terms: 0.3636363636 + 0.2975206612 = 0.6611570248 0.2975206612 + -1.090909091y + y2 = 0.6611570248 Factor a perfect square on the left side: (y + -0.5454545455)(y + -0.5454545455) = 0.6611570248 Calculate the square root of the right side: 0.813115628 Break this problem into two subproblems by setting (y + -0.5454545455) equal to 0.813115628 and -0.813115628.Subproblem 1
y + -0.5454545455 = 0.813115628 Simplifying y + -0.5454545455 = 0.813115628 Reorder the terms: -0.5454545455 + y = 0.813115628 Solving -0.5454545455 + y = 0.813115628 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 = 0.813115628 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = 0.813115628 + 0.5454545455 y = 0.813115628 + 0.5454545455 Combine like terms: 0.813115628 + 0.5454545455 = 1.3585701735 y = 1.3585701735 Simplifying y = 1.3585701735Subproblem 2
y + -0.5454545455 = -0.813115628 Simplifying y + -0.5454545455 = -0.813115628 Reorder the terms: -0.5454545455 + y = -0.813115628 Solving -0.5454545455 + y = -0.813115628 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 = -0.813115628 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = -0.813115628 + 0.5454545455 y = -0.813115628 + 0.5454545455 Combine like terms: -0.813115628 + 0.5454545455 = -0.2676610825 y = -0.2676610825 Simplifying y = -0.2676610825Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3585701735, -0.2676610825}
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