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Simplifying 2y + 2(y + -6) = 7y + -5y(y + -10) Reorder the terms: 2y + 2(-6 + y) = 7y + -5y(y + -10) 2y + (-6 * 2 + y * 2) = 7y + -5y(y + -10) 2y + (-12 + 2y) = 7y + -5y(y + -10) Reorder the terms: -12 + 2y + 2y = 7y + -5y(y + -10) Combine like terms: 2y + 2y = 4y -12 + 4y = 7y + -5y(y + -10) Reorder the terms: -12 + 4y = 7y + -5y(-10 + y) -12 + 4y = 7y + (-10 * -5y + y * -5y) -12 + 4y = 7y + (50y + -5y2) Combine like terms: 7y + 50y = 57y -12 + 4y = 57y + -5y2 Solving -12 + 4y = 57y + -5y2 Solving for variable 'y'. Combine like terms: 4y + -57y = -53y -12 + -53y + 5y2 = 57y + -5y2 + -57y + 5y2 Reorder the terms: -12 + -53y + 5y2 = 57y + -57y + -5y2 + 5y2 Combine like terms: 57y + -57y = 0 -12 + -53y + 5y2 = 0 + -5y2 + 5y2 -12 + -53y + 5y2 = -5y2 + 5y2 Combine like terms: -5y2 + 5y2 = 0 -12 + -53y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -10.6y + y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -10.6y + 2.4 + y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -10.6y + y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -10.6y + y2 = 0 + 2.4 -10.6y + y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -10.6y + y2 = 2.4 The y term is -10.6y. Take half its coefficient (-5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. -10.6y + 28.09 + y2 = 2.4 + 28.09 Reorder the terms: 28.09 + -10.6y + y2 = 2.4 + 28.09 Combine like terms: 2.4 + 28.09 = 30.49 28.09 + -10.6y + y2 = 30.49 Factor a perfect square on the left side: (y + -5.3)(y + -5.3) = 30.49 Calculate the square root of the right side: 5.521775077 Break this problem into two subproblems by setting (y + -5.3) equal to 5.521775077 and -5.521775077.Subproblem 1
y + -5.3 = 5.521775077 Simplifying y + -5.3 = 5.521775077 Reorder the terms: -5.3 + y = 5.521775077 Solving -5.3 + y = 5.521775077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.3' to each side of the equation. -5.3 + 5.3 + y = 5.521775077 + 5.3 Combine like terms: -5.3 + 5.3 = 0.0 0.0 + y = 5.521775077 + 5.3 y = 5.521775077 + 5.3 Combine like terms: 5.521775077 + 5.3 = 10.821775077 y = 10.821775077 Simplifying y = 10.821775077Subproblem 2
y + -5.3 = -5.521775077 Simplifying y + -5.3 = -5.521775077 Reorder the terms: -5.3 + y = -5.521775077 Solving -5.3 + y = -5.521775077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.3' to each side of the equation. -5.3 + 5.3 + y = -5.521775077 + 5.3 Combine like terms: -5.3 + 5.3 = 0.0 0.0 + y = -5.521775077 + 5.3 y = -5.521775077 + 5.3 Combine like terms: -5.521775077 + 5.3 = -0.221775077 y = -0.221775077 Simplifying y = -0.221775077Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.821775077, -0.221775077}
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