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Simplifying 3y2 + 12y = -4 Reorder the terms: 12y + 3y2 = -4 Solving 12y + 3y2 = -4 Solving for variable 'y'. Reorder the terms: 4 + 12y + 3y2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 12y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 4y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 4y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 4y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 4y + y2 = 0 + -1.333333333 4y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 4y + y2 = -1.333333333 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = -1.333333333 + 4 Reorder the terms: 4 + 4y + y2 = -1.333333333 + 4 Combine like terms: -1.333333333 + 4 = 2.666666667 4 + 4y + y2 = 2.666666667 Factor a perfect square on the left side: (y + 2)(y + 2) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (y + 2) equal to 1.632993162 and -1.632993162.Subproblem 1
y + 2 = 1.632993162 Simplifying y + 2 = 1.632993162 Reorder the terms: 2 + y = 1.632993162 Solving 2 + y = 1.632993162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 1.632993162 + -2 Combine like terms: 2 + -2 = 0 0 + y = 1.632993162 + -2 y = 1.632993162 + -2 Combine like terms: 1.632993162 + -2 = -0.367006838 y = -0.367006838 Simplifying y = -0.367006838Subproblem 2
y + 2 = -1.632993162 Simplifying y + 2 = -1.632993162 Reorder the terms: 2 + y = -1.632993162 Solving 2 + y = -1.632993162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -1.632993162 + -2 Combine like terms: 2 + -2 = 0 0 + y = -1.632993162 + -2 y = -1.632993162 + -2 Combine like terms: -1.632993162 + -2 = -3.632993162 y = -3.632993162 Simplifying y = -3.632993162Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.367006838, -3.632993162}
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