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Simplifying 3y2 + y + -28 = 0 Reorder the terms: -28 + y + 3y2 = 0 Solving -28 + y + 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'. -9.333333333 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + 0.3333333333y + 9.333333333 + y2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + 0.3333333333y + y2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + 0.3333333333y + y2 = 0 + 9.333333333 0.3333333333y + y2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 0.3333333333y + y2 = 9.333333333 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333y + 0.25 + y2 = 9.333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = 9.333333333 + 0.25 Combine like terms: 9.333333333 + 0.25 = 9.583333333 0.25 + 0.3333333333y + y2 = 9.583333333 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 9.583333333 Calculate the square root of the right side: 3.095695937 Break this problem into two subproblems by setting (y + 0.5) equal to 3.095695937 and -3.095695937.Subproblem 1
y + 0.5 = 3.095695937 Simplifying y + 0.5 = 3.095695937 Reorder the terms: 0.5 + y = 3.095695937 Solving 0.5 + y = 3.095695937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.095695937 + -0.5 y = 3.095695937 + -0.5 Combine like terms: 3.095695937 + -0.5 = 2.595695937 y = 2.595695937 Simplifying y = 2.595695937Subproblem 2
y + 0.5 = -3.095695937 Simplifying y + 0.5 = -3.095695937 Reorder the terms: 0.5 + y = -3.095695937 Solving 0.5 + y = -3.095695937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.095695937 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.095695937 + -0.5 y = -3.095695937 + -0.5 Combine like terms: -3.095695937 + -0.5 = -3.595695937 y = -3.595695937 Simplifying y = -3.595695937Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.595695937, -3.595695937}
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