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Simplifying 3y2 = 10 + 5y Solving 3y2 = 10 + 5y Solving for variable 'y'. Reorder the terms: -10 + -5y + 3y2 = 10 + 5y + -10 + -5y Reorder the terms: -10 + -5y + 3y2 = 10 + -10 + 5y + -5y Combine like terms: 10 + -10 = 0 -10 + -5y + 3y2 = 0 + 5y + -5y -10 + -5y + 3y2 = 5y + -5y Combine like terms: 5y + -5y = 0 -10 + -5y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -1.666666667y + y2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1.666666667y + 3.333333333 + y2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1.666666667y + y2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1.666666667y + y2 = 0 + 3.333333333 -1.666666667y + y2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1.666666667y + y2 = 3.333333333 The y term is -1.666666667y. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667y + 0.6944444447 + y2 = 3.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667y + y2 = 3.333333333 + 0.6944444447 Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777 0.6944444447 + -1.666666667y + y2 = 4.0277777777 Factor a perfect square on the left side: (y + -0.8333333335)(y + -0.8333333335) = 4.0277777777 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (y + -0.8333333335) equal to 2.00693243 and -2.00693243.Subproblem 1
y + -0.8333333335 = 2.00693243 Simplifying y + -0.8333333335 = 2.00693243 Reorder the terms: -0.8333333335 + y = 2.00693243 Solving -0.8333333335 + y = 2.00693243 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y = 2.00693243 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y = 2.00693243 + 0.8333333335 y = 2.00693243 + 0.8333333335 Combine like terms: 2.00693243 + 0.8333333335 = 2.8402657635 y = 2.8402657635 Simplifying y = 2.8402657635Subproblem 2
y + -0.8333333335 = -2.00693243 Simplifying y + -0.8333333335 = -2.00693243 Reorder the terms: -0.8333333335 + y = -2.00693243 Solving -0.8333333335 + y = -2.00693243 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y = -2.00693243 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y = -2.00693243 + 0.8333333335 y = -2.00693243 + 0.8333333335 Combine like terms: -2.00693243 + 0.8333333335 = -1.1735990965 y = -1.1735990965 Simplifying y = -1.1735990965Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.8402657635, -1.1735990965}
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