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Simplifying -9y2 + -29y + -10 = 0 Reorder the terms: -10 + -29y + -9y2 = 0 Solving -10 + -29y + -9y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 29y + 9y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 29y + 9y2)' equal to zero and attempt to solve: Simplifying 10 + 29y + 9y2 = 0 Solving 10 + 29y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.111111111 + 3.222222222y + y2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + 3.222222222y + -1.111111111 + y2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + 3.222222222y + y2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + 3.222222222y + y2 = 0 + -1.111111111 3.222222222y + y2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 3.222222222y + y2 = -1.111111111 The y term is 3.222222222y. Take half its coefficient (1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. 3.222222222y + 2.595679012 + y2 = -1.111111111 + 2.595679012 Reorder the terms: 2.595679012 + 3.222222222y + y2 = -1.111111111 + 2.595679012 Combine like terms: -1.111111111 + 2.595679012 = 1.484567901 2.595679012 + 3.222222222y + y2 = 1.484567901 Factor a perfect square on the left side: (y + 1.611111111)(y + 1.611111111) = 1.484567901 Calculate the square root of the right side: 1.218428455 Break this problem into two subproblems by setting (y + 1.611111111) equal to 1.218428455 and -1.218428455.Subproblem 1
y + 1.611111111 = 1.218428455 Simplifying y + 1.611111111 = 1.218428455 Reorder the terms: 1.611111111 + y = 1.218428455 Solving 1.611111111 + y = 1.218428455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + y = 1.218428455 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + y = 1.218428455 + -1.611111111 y = 1.218428455 + -1.611111111 Combine like terms: 1.218428455 + -1.611111111 = -0.392682656 y = -0.392682656 Simplifying y = -0.392682656Subproblem 2
y + 1.611111111 = -1.218428455 Simplifying y + 1.611111111 = -1.218428455 Reorder the terms: 1.611111111 + y = -1.218428455 Solving 1.611111111 + y = -1.218428455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + y = -1.218428455 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + y = -1.218428455 + -1.611111111 y = -1.218428455 + -1.611111111 Combine like terms: -1.218428455 + -1.611111111 = -2.829539566 y = -2.829539566 Simplifying y = -2.829539566Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.392682656, -2.829539566}Solution
y = {-0.392682656, -2.829539566}
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