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Simplifying (5y2 + -1y + -2) + (4y2 + -7y + 3) = 0 Reorder the terms: (-2 + -1y + 5y2) + (4y2 + -7y + 3) = 0 Remove parenthesis around (-2 + -1y + 5y2) -2 + -1y + 5y2 + (4y2 + -7y + 3) = 0 Reorder the terms: -2 + -1y + 5y2 + (3 + -7y + 4y2) = 0 Remove parenthesis around (3 + -7y + 4y2) -2 + -1y + 5y2 + 3 + -7y + 4y2 = 0 Reorder the terms: -2 + 3 + -1y + -7y + 5y2 + 4y2 = 0 Combine like terms: -2 + 3 = 1 1 + -1y + -7y + 5y2 + 4y2 = 0 Combine like terms: -1y + -7y = -8y 1 + -8y + 5y2 + 4y2 = 0 Combine like terms: 5y2 + 4y2 = 9y2 1 + -8y + 9y2 = 0 Solving 1 + -8y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -0.8888888889y + y2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.8888888889y + -0.1111111111 + y2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -0.8888888889y + y2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -0.8888888889y + y2 = 0 + -0.1111111111 -0.8888888889y + y2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -0.8888888889y + y2 = -0.1111111111 The y term is -0.8888888889y. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889y + 0.1975308642 + y2 = -0.1111111111 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889y + y2 = -0.1111111111 + 0.1975308642 Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531 0.1975308642 + -0.8888888889y + y2 = 0.0864197531 Factor a perfect square on the left side: (y + -0.4444444445)(y + -0.4444444445) = 0.0864197531 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (y + -0.4444444445) equal to 0.293972368 and -0.293972368.Subproblem 1
y + -0.4444444445 = 0.293972368 Simplifying y + -0.4444444445 = 0.293972368 Reorder the terms: -0.4444444445 + y = 0.293972368 Solving -0.4444444445 + y = 0.293972368 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + y = 0.293972368 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = 0.293972368 + 0.4444444445 y = 0.293972368 + 0.4444444445 Combine like terms: 0.293972368 + 0.4444444445 = 0.7384168125 y = 0.7384168125 Simplifying y = 0.7384168125Subproblem 2
y + -0.4444444445 = -0.293972368 Simplifying y + -0.4444444445 = -0.293972368 Reorder the terms: -0.4444444445 + y = -0.293972368 Solving -0.4444444445 + y = -0.293972368 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + y = -0.293972368 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = -0.293972368 + 0.4444444445 y = -0.293972368 + 0.4444444445 Combine like terms: -0.293972368 + 0.4444444445 = 0.1504720765 y = 0.1504720765 Simplifying y = 0.1504720765Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.7384168125, 0.1504720765}
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