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Simplifying 3y2 + -6y = 8 Reorder the terms: -6y + 3y2 = 8 Solving -6y + 3y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + -6y + 3y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -6y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -2y + y2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -2y + 2.666666667 + y2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -2y + y2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -2y + y2 = 0 + 2.666666667 -2y + y2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -2y + y2 = 2.666666667 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 2.666666667 + 1 Reorder the terms: 1 + -2y + y2 = 2.666666667 + 1 Combine like terms: 2.666666667 + 1 = 3.666666667 1 + -2y + y2 = 3.666666667 Factor a perfect square on the left side: (y + -1)(y + -1) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (y + -1) equal to 1.914854216 and -1.914854216.Subproblem 1
y + -1 = 1.914854216 Simplifying y + -1 = 1.914854216 Reorder the terms: -1 + y = 1.914854216 Solving -1 + y = 1.914854216 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.914854216 + 1 y = 1.914854216 + 1 Combine like terms: 1.914854216 + 1 = 2.914854216 y = 2.914854216 Simplifying y = 2.914854216Subproblem 2
y + -1 = -1.914854216 Simplifying y + -1 = -1.914854216 Reorder the terms: -1 + y = -1.914854216 Solving -1 + y = -1.914854216 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.914854216 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.914854216 + 1 y = -1.914854216 + 1 Combine like terms: -1.914854216 + 1 = -0.914854216 y = -0.914854216 Simplifying y = -0.914854216Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.914854216, -0.914854216}
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