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Simplifying 6y2 + -2y = 3 Reorder the terms: -2y + 6y2 = 3 Solving -2y + 6y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + -2y + 6y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -2y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -0.3333333333y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.3333333333y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.3333333333y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.3333333333y + y2 = 0 + 0.5 -0.3333333333y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.3333333333y + y2 = 0.5 The y term is -0.3333333333y. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333y + 0.02777777779 + y2 = 0.5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333y + y2 = 0.5 + 0.02777777779 Combine like terms: 0.5 + 0.02777777779 = 0.52777777779 0.02777777779 + -0.3333333333y + y2 = 0.52777777779 Factor a perfect square on the left side: (y + -0.1666666667)(y + -0.1666666667) = 0.52777777779 Calculate the square root of the right side: 0.726483157 Break this problem into two subproblems by setting (y + -0.1666666667) equal to 0.726483157 and -0.726483157.Subproblem 1
y + -0.1666666667 = 0.726483157 Simplifying y + -0.1666666667 = 0.726483157 Reorder the terms: -0.1666666667 + y = 0.726483157 Solving -0.1666666667 + y = 0.726483157 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + y = 0.726483157 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = 0.726483157 + 0.1666666667 y = 0.726483157 + 0.1666666667 Combine like terms: 0.726483157 + 0.1666666667 = 0.8931498237 y = 0.8931498237 Simplifying y = 0.8931498237Subproblem 2
y + -0.1666666667 = -0.726483157 Simplifying y + -0.1666666667 = -0.726483157 Reorder the terms: -0.1666666667 + y = -0.726483157 Solving -0.1666666667 + y = -0.726483157 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + y = -0.726483157 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = -0.726483157 + 0.1666666667 y = -0.726483157 + 0.1666666667 Combine like terms: -0.726483157 + 0.1666666667 = -0.5598164903 y = -0.5598164903 Simplifying y = -0.5598164903Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8931498237, -0.5598164903}
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