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Simplifying 3y2 + 4y = 240 Reorder the terms: 4y + 3y2 = 240 Solving 4y + 3y2 = 240 Solving for variable 'y'. Reorder the terms: -240 + 4y + 3y2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -80 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 1.333333333y + 80 + y2 = 0 + 80 Reorder the terms: -80 + 80 + 1.333333333y + y2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 1.333333333y + y2 = 0 + 80 1.333333333y + y2 = 0 + 80 Combine like terms: 0 + 80 = 80 1.333333333y + y2 = 80 The y term is 1.333333333y. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333y + 0.4444444442 + y2 = 80 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = 80 + 0.4444444442 Combine like terms: 80 + 0.4444444442 = 80.4444444442 0.4444444442 + 1.333333333y + y2 = 80.4444444442 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = 80.4444444442 Calculate the square root of the right side: 8.969082698 Break this problem into two subproblems by setting (y + 0.6666666665) equal to 8.969082698 and -8.969082698.Subproblem 1
y + 0.6666666665 = 8.969082698 Simplifying y + 0.6666666665 = 8.969082698 Reorder the terms: 0.6666666665 + y = 8.969082698 Solving 0.6666666665 + y = 8.969082698 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y = 8.969082698 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = 8.969082698 + -0.6666666665 y = 8.969082698 + -0.6666666665 Combine like terms: 8.969082698 + -0.6666666665 = 8.3024160315 y = 8.3024160315 Simplifying y = 8.3024160315Subproblem 2
y + 0.6666666665 = -8.969082698 Simplifying y + 0.6666666665 = -8.969082698 Reorder the terms: 0.6666666665 + y = -8.969082698 Solving 0.6666666665 + y = -8.969082698 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y = -8.969082698 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = -8.969082698 + -0.6666666665 y = -8.969082698 + -0.6666666665 Combine like terms: -8.969082698 + -0.6666666665 = -9.6357493645 y = -9.6357493645 Simplifying y = -9.6357493645Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.3024160315, -9.6357493645}
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