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Simplifying 3y2 + -6y + -8 = 21 Reorder the terms: -8 + -6y + 3y2 = 21 Solving -8 + -6y + 3y2 = 21 Solving for variable 'y'. Reorder the terms: -8 + -21 + -6y + 3y2 = 21 + -21 Combine like terms: -8 + -21 = -29 -29 + -6y + 3y2 = 21 + -21 Combine like terms: 21 + -21 = 0 -29 + -6y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.666666667 + -2y + y2 = 0 Move the constant term to the right: Add '9.666666667' to each side of the equation. -9.666666667 + -2y + 9.666666667 + y2 = 0 + 9.666666667 Reorder the terms: -9.666666667 + 9.666666667 + -2y + y2 = 0 + 9.666666667 Combine like terms: -9.666666667 + 9.666666667 = 0.000000000 0.000000000 + -2y + y2 = 0 + 9.666666667 -2y + y2 = 0 + 9.666666667 Combine like terms: 0 + 9.666666667 = 9.666666667 -2y + y2 = 9.666666667 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 = 9.666666667 + 1 Reorder the terms: 1 + -2y + y2 = 9.666666667 + 1 Combine like terms: 9.666666667 + 1 = 10.666666667 1 + -2y + y2 = 10.666666667 Factor a perfect square on the left side: (y + -1)(y + -1) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (y + -1) equal to 3.265986324 and -3.265986324.Subproblem 1
y + -1 = 3.265986324 Simplifying y + -1 = 3.265986324 Reorder the terms: -1 + y = 3.265986324 Solving -1 + y = 3.265986324 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 = 3.265986324 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.265986324 + 1 y = 3.265986324 + 1 Combine like terms: 3.265986324 + 1 = 4.265986324 y = 4.265986324 Simplifying y = 4.265986324Subproblem 2
y + -1 = -3.265986324 Simplifying y + -1 = -3.265986324 Reorder the terms: -1 + y = -3.265986324 Solving -1 + y = -3.265986324 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 = -3.265986324 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.265986324 + 1 y = -3.265986324 + 1 Combine like terms: -3.265986324 + 1 = -2.265986324 y = -2.265986324 Simplifying y = -2.265986324Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.265986324, -2.265986324}
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