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Simplifying 3y2 + -2y + -3y2 + 5y2 + -1 + 6y2 = 0 Reorder the terms: -1 + -2y + 3y2 + -3y2 + 5y2 + 6y2 = 0 Combine like terms: 3y2 + -3y2 = 0 -1 + -2y + 0 + 5y2 + 6y2 = 0 -1 + -2y + 5y2 + 6y2 = 0 Combine like terms: 5y2 + 6y2 = 11y2 -1 + -2y + 11y2 = 0 Solving -1 + -2y + 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'. -0.09090909091 + -0.1818181818y + y2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.1818181818y + 0.09090909091 + y2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.1818181818y + y2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.1818181818y + y2 = 0 + 0.09090909091 -0.1818181818y + y2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.1818181818y + y2 = 0.09090909091 The y term is -0.1818181818y. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818y + 0.008264462808 + y2 = 0.09090909091 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818y + y2 = 0.09090909091 + 0.008264462808 Combine like terms: 0.09090909091 + 0.008264462808 = 0.099173553718 0.008264462808 + -0.1818181818y + y2 = 0.099173553718 Factor a perfect square on the left side: (y + -0.0909090909)(y + -0.0909090909) = 0.099173553718 Calculate the square root of the right side: 0.314918329 Break this problem into two subproblems by setting (y + -0.0909090909) equal to 0.314918329 and -0.314918329.Subproblem 1
y + -0.0909090909 = 0.314918329 Simplifying y + -0.0909090909 = 0.314918329 Reorder the terms: -0.0909090909 + y = 0.314918329 Solving -0.0909090909 + y = 0.314918329 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + y = 0.314918329 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + y = 0.314918329 + 0.0909090909 y = 0.314918329 + 0.0909090909 Combine like terms: 0.314918329 + 0.0909090909 = 0.4058274199 y = 0.4058274199 Simplifying y = 0.4058274199Subproblem 2
y + -0.0909090909 = -0.314918329 Simplifying y + -0.0909090909 = -0.314918329 Reorder the terms: -0.0909090909 + y = -0.314918329 Solving -0.0909090909 + y = -0.314918329 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + y = -0.314918329 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + y = -0.314918329 + 0.0909090909 y = -0.314918329 + 0.0909090909 Combine like terms: -0.314918329 + 0.0909090909 = -0.2240092381 y = -0.2240092381 Simplifying y = -0.2240092381Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4058274199, -0.2240092381}
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