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Simplifying (2y2 + -8y + -5) + -1(6y2 + 8y + -7) = 0 Reorder the terms: (-5 + -8y + 2y2) + -1(6y2 + 8y + -7) = 0 Remove parenthesis around (-5 + -8y + 2y2) -5 + -8y + 2y2 + -1(6y2 + 8y + -7) = 0 Reorder the terms: -5 + -8y + 2y2 + -1(-7 + 8y + 6y2) = 0 -5 + -8y + 2y2 + (-7 * -1 + 8y * -1 + 6y2 * -1) = 0 -5 + -8y + 2y2 + (7 + -8y + -6y2) = 0 Reorder the terms: -5 + 7 + -8y + -8y + 2y2 + -6y2 = 0 Combine like terms: -5 + 7 = 2 2 + -8y + -8y + 2y2 + -6y2 = 0 Combine like terms: -8y + -8y = -16y 2 + -16y + 2y2 + -6y2 = 0 Combine like terms: 2y2 + -6y2 = -4y2 2 + -16y + -4y2 = 0 Solving 2 + -16y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -8y + -2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8y + -2y2)' equal to zero and attempt to solve: Simplifying 1 + -8y + -2y2 = 0 Solving 1 + -8y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 4y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4y + y2 = 0 + 0.5 4y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4y + y2 = 0.5 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 0.5 + 4 Reorder the terms: 4 + 4y + y2 = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 4 + 4y + y2 = 4.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (y + 2) equal to 2.121320344 and -2.121320344.Subproblem 1
y + 2 = 2.121320344 Simplifying y + 2 = 2.121320344 Reorder the terms: 2 + y = 2.121320344 Solving 2 + y = 2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.121320344 + -2 y = 2.121320344 + -2 Combine like terms: 2.121320344 + -2 = 0.121320344 y = 0.121320344 Simplifying y = 0.121320344Subproblem 2
y + 2 = -2.121320344 Simplifying y + 2 = -2.121320344 Reorder the terms: 2 + y = -2.121320344 Solving 2 + y = -2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.121320344 + -2 y = -2.121320344 + -2 Combine like terms: -2.121320344 + -2 = -4.121320344 y = -4.121320344 Simplifying y = -4.121320344Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.121320344, -4.121320344}Solution
y = {0.121320344, -4.121320344}
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