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Simplifying 4y + 3y2 = 21 Solving 4y + 3y2 = 21 Solving for variable 'y'. Reorder the terms: -21 + 4y + 3y2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 1.333333333y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + 1.333333333y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1.333333333y + y2 = 0 + 7 1.333333333y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 1.333333333y + y2 = 7 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 = 7 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = 7 + 0.4444444442 Combine like terms: 7 + 0.4444444442 = 7.4444444442 0.4444444442 + 1.333333333y + y2 = 7.4444444442 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = 7.4444444442 Calculate the square root of the right side: 2.728450924 Break this problem into two subproblems by setting (y + 0.6666666665) equal to 2.728450924 and -2.728450924.Subproblem 1
y + 0.6666666665 = 2.728450924 Simplifying y + 0.6666666665 = 2.728450924 Reorder the terms: 0.6666666665 + y = 2.728450924 Solving 0.6666666665 + y = 2.728450924 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 = 2.728450924 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = 2.728450924 + -0.6666666665 y = 2.728450924 + -0.6666666665 Combine like terms: 2.728450924 + -0.6666666665 = 2.0617842575 y = 2.0617842575 Simplifying y = 2.0617842575Subproblem 2
y + 0.6666666665 = -2.728450924 Simplifying y + 0.6666666665 = -2.728450924 Reorder the terms: 0.6666666665 + y = -2.728450924 Solving 0.6666666665 + y = -2.728450924 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 = -2.728450924 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = -2.728450924 + -0.6666666665 y = -2.728450924 + -0.6666666665 Combine like terms: -2.728450924 + -0.6666666665 = -3.3951175905 y = -3.3951175905 Simplifying y = -3.3951175905Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.0617842575, -3.3951175905}
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