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Simplifying 3y2 + 6 = 10y Reorder the terms: 6 + 3y2 = 10y Solving 6 + 3y2 = 10y Solving for variable 'y'. Reorder the terms: 6 + -10y + 3y2 = 10y + -10y Combine like terms: 10y + -10y = 0 6 + -10y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + -3.333333333y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.333333333y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -3.333333333y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.333333333y + y2 = 0 + -2 -3.333333333y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.333333333y + y2 = -2 The y term is -3.333333333y. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333y + 2.777777779 + y2 = -2 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333y + y2 = -2 + 2.777777779 Combine like terms: -2 + 2.777777779 = 0.777777779 2.777777779 + -3.333333333y + y2 = 0.777777779 Factor a perfect square on the left side: (y + -1.666666667)(y + -1.666666667) = 0.777777779 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (y + -1.666666667) equal to 0.881917104 and -0.881917104.Subproblem 1
y + -1.666666667 = 0.881917104 Simplifying y + -1.666666667 = 0.881917104 Reorder the terms: -1.666666667 + y = 0.881917104 Solving -1.666666667 + y = 0.881917104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = 0.881917104 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = 0.881917104 + 1.666666667 y = 0.881917104 + 1.666666667 Combine like terms: 0.881917104 + 1.666666667 = 2.548583771 y = 2.548583771 Simplifying y = 2.548583771Subproblem 2
y + -1.666666667 = -0.881917104 Simplifying y + -1.666666667 = -0.881917104 Reorder the terms: -1.666666667 + y = -0.881917104 Solving -1.666666667 + y = -0.881917104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = -0.881917104 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = -0.881917104 + 1.666666667 y = -0.881917104 + 1.666666667 Combine like terms: -0.881917104 + 1.666666667 = 0.784749563 y = 0.784749563 Simplifying y = 0.784749563Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.548583771, 0.784749563}
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