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Simplifying (-6y2 + 5y + 8) + -1(8y + 1) = 0 Reorder the terms: (8 + 5y + -6y2) + -1(8y + 1) = 0 Remove parenthesis around (8 + 5y + -6y2) 8 + 5y + -6y2 + -1(8y + 1) = 0 Reorder the terms: 8 + 5y + -6y2 + -1(1 + 8y) = 0 8 + 5y + -6y2 + (1 * -1 + 8y * -1) = 0 8 + 5y + -6y2 + (-1 + -8y) = 0 Reorder the terms: 8 + -1 + 5y + -8y + -6y2 = 0 Combine like terms: 8 + -1 = 7 7 + 5y + -8y + -6y2 = 0 Combine like terms: 5y + -8y = -3y 7 + -3y + -6y2 = 0 Solving 7 + -3y + -6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + 0.5y + y2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.5y + 1.166666667 + y2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.5y + y2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.5y + y2 = 0 + 1.166666667 0.5y + y2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.5y + y2 = 1.166666667 The y term is 0.5y. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y + 0.0625 + y2 = 1.166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5y + y2 = 1.166666667 + 0.0625 Combine like terms: 1.166666667 + 0.0625 = 1.229166667 0.0625 + 0.5y + y2 = 1.229166667 Factor a perfect square on the left side: (y + 0.25)(y + 0.25) = 1.229166667 Calculate the square root of the right side: 1.108677891 Break this problem into two subproblems by setting (y + 0.25) equal to 1.108677891 and -1.108677891.Subproblem 1
y + 0.25 = 1.108677891 Simplifying y + 0.25 = 1.108677891 Reorder the terms: 0.25 + y = 1.108677891 Solving 0.25 + y = 1.108677891 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = 1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = 1.108677891 + -0.25 y = 1.108677891 + -0.25 Combine like terms: 1.108677891 + -0.25 = 0.858677891 y = 0.858677891 Simplifying y = 0.858677891Subproblem 2
y + 0.25 = -1.108677891 Simplifying y + 0.25 = -1.108677891 Reorder the terms: 0.25 + y = -1.108677891 Solving 0.25 + y = -1.108677891 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = -1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = -1.108677891 + -0.25 y = -1.108677891 + -0.25 Combine like terms: -1.108677891 + -0.25 = -1.358677891 y = -1.358677891 Simplifying y = -1.358677891Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.858677891, -1.358677891}
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