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Simplifying 3y2 + 5y + -10 = 0 Reorder the terms: -10 + 5y + 3y2 = 0 Solving -10 + 5y + 3y2 = 0 Solving for variable 'y'. 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 = 1.1735990965 y = 1.1735990965 Simplifying y = 1.1735990965Subproblem 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 = -2.8402657635 y = -2.8402657635 Simplifying y = -2.8402657635Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.1735990965, -2.8402657635}
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