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Simplifying (2y2 + 7y + 11) + -1(8y2 + -5y + 7) = 0 Reorder the terms: (11 + 7y + 2y2) + -1(8y2 + -5y + 7) = 0 Remove parenthesis around (11 + 7y + 2y2) 11 + 7y + 2y2 + -1(8y2 + -5y + 7) = 0 Reorder the terms: 11 + 7y + 2y2 + -1(7 + -5y + 8y2) = 0 11 + 7y + 2y2 + (7 * -1 + -5y * -1 + 8y2 * -1) = 0 11 + 7y + 2y2 + (-7 + 5y + -8y2) = 0 Reorder the terms: 11 + -7 + 7y + 5y + 2y2 + -8y2 = 0 Combine like terms: 11 + -7 = 4 4 + 7y + 5y + 2y2 + -8y2 = 0 Combine like terms: 7y + 5y = 12y 4 + 12y + 2y2 + -8y2 = 0 Combine like terms: 2y2 + -8y2 = -6y2 4 + 12y + -6y2 = 0 Solving 4 + 12y + -6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 6y + -3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 6y + -3y2)' equal to zero and attempt to solve: Simplifying 2 + 6y + -3y2 = 0 Solving 2 + 6y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -2y + y2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2y + 0.6666666667 + y2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2y + y2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2y + y2 = 0 + 0.6666666667 -2y + y2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2y + y2 = 0.6666666667 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 0.6666666667 + 1 Reorder the terms: 1 + -2y + y2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + -2y + y2 = 1.6666666667 Factor a perfect square on the left side: (y + -1)(y + -1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (y + -1) equal to 1.290994449 and -1.290994449.Subproblem 1
y + -1 = 1.290994449 Simplifying y + -1 = 1.290994449 Reorder the terms: -1 + y = 1.290994449 Solving -1 + y = 1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.290994449 + 1 y = 1.290994449 + 1 Combine like terms: 1.290994449 + 1 = 2.290994449 y = 2.290994449 Simplifying y = 2.290994449Subproblem 2
y + -1 = -1.290994449 Simplifying y + -1 = -1.290994449 Reorder the terms: -1 + y = -1.290994449 Solving -1 + y = -1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.290994449 + 1 y = -1.290994449 + 1 Combine like terms: -1.290994449 + 1 = -0.290994449 y = -0.290994449 Simplifying y = -0.290994449Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.290994449, -0.290994449}Solution
y = {2.290994449, -0.290994449}
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