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Simplifying (4y2 + 7y + -5) + -1(5y2 + -3y + -7) = 0 Reorder the terms: (-5 + 7y + 4y2) + -1(5y2 + -3y + -7) = 0 Remove parenthesis around (-5 + 7y + 4y2) -5 + 7y + 4y2 + -1(5y2 + -3y + -7) = 0 Reorder the terms: -5 + 7y + 4y2 + -1(-7 + -3y + 5y2) = 0 -5 + 7y + 4y2 + (-7 * -1 + -3y * -1 + 5y2 * -1) = 0 -5 + 7y + 4y2 + (7 + 3y + -5y2) = 0 Reorder the terms: -5 + 7 + 7y + 3y + 4y2 + -5y2 = 0 Combine like terms: -5 + 7 = 2 2 + 7y + 3y + 4y2 + -5y2 = 0 Combine like terms: 7y + 3y = 10y 2 + 10y + 4y2 + -5y2 = 0 Combine like terms: 4y2 + -5y2 = -1y2 2 + 10y + -1y2 = 0 Solving 2 + 10y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -10y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -10y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -10y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -10y + y2 = 0 + 2 -10y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -10y + y2 = 2 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 2 + 25 Reorder the terms: 25 + -10y + y2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + -10y + y2 = 27 Factor a perfect square on the left side: (y + -5)(y + -5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -5) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -5 = 5.196152423 Simplifying y + -5 = 5.196152423 Reorder the terms: -5 + y = 5.196152423 Solving -5 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + y = 5.196152423 + 5 y = 5.196152423 + 5 Combine like terms: 5.196152423 + 5 = 10.196152423 y = 10.196152423 Simplifying y = 10.196152423Subproblem 2
y + -5 = -5.196152423 Simplifying y + -5 = -5.196152423 Reorder the terms: -5 + y = -5.196152423 Solving -5 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + y = -5.196152423 + 5 y = -5.196152423 + 5 Combine like terms: -5.196152423 + 5 = -0.196152423 y = -0.196152423 Simplifying y = -0.196152423Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.196152423, -0.196152423}
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