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Simplifying 3y2 + y + -20 = 0 Reorder the terms: -20 + y + 3y2 = 0 Solving -20 + 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'. -6.666666667 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 0.3333333333y + 6.666666667 + y2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 0.3333333333y + y2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 0.3333333333y + y2 = 0 + 6.666666667 0.3333333333y + y2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 0.3333333333y + y2 = 6.666666667 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 = 6.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = 6.666666667 + 0.25 Combine like terms: 6.666666667 + 0.25 = 6.916666667 0.25 + 0.3333333333y + y2 = 6.916666667 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 6.916666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (y + 0.5) equal to 2.62995564 and -2.62995564.Subproblem 1
y + 0.5 = 2.62995564 Simplifying y + 0.5 = 2.62995564 Reorder the terms: 0.5 + y = 2.62995564 Solving 0.5 + y = 2.62995564 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 = 2.62995564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.62995564 + -0.5 y = 2.62995564 + -0.5 Combine like terms: 2.62995564 + -0.5 = 2.12995564 y = 2.12995564 Simplifying y = 2.12995564Subproblem 2
y + 0.5 = -2.62995564 Simplifying y + 0.5 = -2.62995564 Reorder the terms: 0.5 + y = -2.62995564 Solving 0.5 + y = -2.62995564 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 = -2.62995564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.62995564 + -0.5 y = -2.62995564 + -0.5 Combine like terms: -2.62995564 + -0.5 = -3.12995564 y = -3.12995564 Simplifying y = -3.12995564Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.12995564, -3.12995564}
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