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Simplifying 13y + 3 = 12y2 Reorder the terms: 3 + 13y = 12y2 Solving 3 + 13y = 12y2 Solving for variable 'y'. Combine like terms: 12y2 + -12y2 = 0 3 + 13y + -12y2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.25 + -1.083333333y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.083333333y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.083333333y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.083333333y + y2 = 0 + 0.25 -1.083333333y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.083333333y + y2 = 0.25 The y term is -1.083333333y. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333y + 0.2934027776 + y2 = 0.25 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333y + y2 = 0.25 + 0.2934027776 Combine like terms: 0.25 + 0.2934027776 = 0.5434027776 0.2934027776 + -1.083333333y + y2 = 0.5434027776 Factor a perfect square on the left side: (y + -0.5416666665)(y + -0.5416666665) = 0.5434027776 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (y + -0.5416666665) equal to 0.737158584 and -0.737158584.Subproblem 1
y + -0.5416666665 = 0.737158584 Simplifying y + -0.5416666665 = 0.737158584 Reorder the terms: -0.5416666665 + y = 0.737158584 Solving -0.5416666665 + y = 0.737158584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + y = 0.737158584 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + y = 0.737158584 + 0.5416666665 y = 0.737158584 + 0.5416666665 Combine like terms: 0.737158584 + 0.5416666665 = 1.2788252505 y = 1.2788252505 Simplifying y = 1.2788252505Subproblem 2
y + -0.5416666665 = -0.737158584 Simplifying y + -0.5416666665 = -0.737158584 Reorder the terms: -0.5416666665 + y = -0.737158584 Solving -0.5416666665 + y = -0.737158584 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + y = -0.737158584 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + y = -0.737158584 + 0.5416666665 y = -0.737158584 + 0.5416666665 Combine like terms: -0.737158584 + 0.5416666665 = -0.1954919175 y = -0.1954919175 Simplifying y = -0.1954919175Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2788252505, -0.1954919175}
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