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Simplifying (-3y2 + -4y + -4) + -1(4y2 + -9y + -8) + (5y2 + 2y + 3) = 0 Reorder the terms: (-4 + -4y + -3y2) + -1(4y2 + -9y + -8) + (5y2 + 2y + 3) = 0 Remove parenthesis around (-4 + -4y + -3y2) -4 + -4y + -3y2 + -1(4y2 + -9y + -8) + (5y2 + 2y + 3) = 0 Reorder the terms: -4 + -4y + -3y2 + -1(-8 + -9y + 4y2) + (5y2 + 2y + 3) = 0 -4 + -4y + -3y2 + (-8 * -1 + -9y * -1 + 4y2 * -1) + (5y2 + 2y + 3) = 0 -4 + -4y + -3y2 + (8 + 9y + -4y2) + (5y2 + 2y + 3) = 0 Reorder the terms: -4 + -4y + -3y2 + 8 + 9y + -4y2 + (3 + 2y + 5y2) = 0 Remove parenthesis around (3 + 2y + 5y2) -4 + -4y + -3y2 + 8 + 9y + -4y2 + 3 + 2y + 5y2 = 0 Reorder the terms: -4 + 8 + 3 + -4y + 9y + 2y + -3y2 + -4y2 + 5y2 = 0 Combine like terms: -4 + 8 = 4 4 + 3 + -4y + 9y + 2y + -3y2 + -4y2 + 5y2 = 0 Combine like terms: 4 + 3 = 7 7 + -4y + 9y + 2y + -3y2 + -4y2 + 5y2 = 0 Combine like terms: -4y + 9y = 5y 7 + 5y + 2y + -3y2 + -4y2 + 5y2 = 0 Combine like terms: 5y + 2y = 7y 7 + 7y + -3y2 + -4y2 + 5y2 = 0 Combine like terms: -3y2 + -4y2 = -7y2 7 + 7y + -7y2 + 5y2 = 0 Combine like terms: -7y2 + 5y2 = -2y2 7 + 7y + -2y2 = 0 Solving 7 + 7y + -2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -3.5y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.5y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.5y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.5y + y2 = 0 + 3.5 -3.5y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.5y + y2 = 3.5 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + -3.5y + y2 = 6.5625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (y + -1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
y + -1.75 = 2.561737691 Simplifying y + -1.75 = 2.561737691 Reorder the terms: -1.75 + y = 2.561737691 Solving -1.75 + y = 2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.561737691 + 1.75 y = 2.561737691 + 1.75 Combine like terms: 2.561737691 + 1.75 = 4.311737691 y = 4.311737691 Simplifying y = 4.311737691Subproblem 2
y + -1.75 = -2.561737691 Simplifying y + -1.75 = -2.561737691 Reorder the terms: -1.75 + y = -2.561737691 Solving -1.75 + y = -2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.561737691 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.561737691 + 1.75 y = -2.561737691 + 1.75 Combine like terms: -2.561737691 + 1.75 = -0.811737691 y = -0.811737691 Simplifying y = -0.811737691Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.311737691, -0.811737691}
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