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Simplifying 3y2 + 24y + -21 = 0 Reorder the terms: -21 + 24y + 3y2 = 0 Solving -21 + 24y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 8y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 8y + y2)' equal to zero and attempt to solve: Simplifying -7 + 8y + y2 = 0 Solving -7 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + 8y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8y + y2 = 0 + 7 8y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 8y + y2 = 7 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 7 + 16 Reorder the terms: 16 + 8y + y2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8y + y2 = 23 Factor a perfect square on the left side: (y + 4)(y + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (y + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
y + 4 = 4.795831523 Simplifying y + 4 = 4.795831523 Reorder the terms: 4 + y = 4.795831523 Solving 4 + y = 4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.795831523 + -4 y = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 y = 0.795831523 Simplifying y = 0.795831523Subproblem 2
y + 4 = -4.795831523 Simplifying y + 4 = -4.795831523 Reorder the terms: 4 + y = -4.795831523 Solving 4 + y = -4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.795831523 + -4 y = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 y = -8.795831523 Simplifying y = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.795831523, -8.795831523}Solution
y = {0.795831523, -8.795831523}
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