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Simplifying 9 + 8y + -3y2 + 6y + 2 + -4y2 = 0 Reorder the terms: 9 + 2 + 8y + 6y + -3y2 + -4y2 = 0 Combine like terms: 9 + 2 = 11 11 + 8y + 6y + -3y2 + -4y2 = 0 Combine like terms: 8y + 6y = 14y 11 + 14y + -3y2 + -4y2 = 0 Combine like terms: -3y2 + -4y2 = -7y2 11 + 14y + -7y2 = 0 Solving 11 + 14y + -7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.571428571 + -2y + y2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -2y + 1.571428571 + y2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -2y + y2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -2y + y2 = 0 + 1.571428571 -2y + y2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -2y + y2 = 1.571428571 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 1.571428571 + 1 Reorder the terms: 1 + -2y + y2 = 1.571428571 + 1 Combine like terms: 1.571428571 + 1 = 2.571428571 1 + -2y + y2 = 2.571428571 Factor a perfect square on the left side: (y + -1)(y + -1) = 2.571428571 Calculate the square root of the right side: 1.603567451 Break this problem into two subproblems by setting (y + -1) equal to 1.603567451 and -1.603567451.Subproblem 1
y + -1 = 1.603567451 Simplifying y + -1 = 1.603567451 Reorder the terms: -1 + y = 1.603567451 Solving -1 + y = 1.603567451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.603567451 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.603567451 + 1 y = 1.603567451 + 1 Combine like terms: 1.603567451 + 1 = 2.603567451 y = 2.603567451 Simplifying y = 2.603567451Subproblem 2
y + -1 = -1.603567451 Simplifying y + -1 = -1.603567451 Reorder the terms: -1 + y = -1.603567451 Solving -1 + y = -1.603567451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.603567451 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.603567451 + 1 y = -1.603567451 + 1 Combine like terms: -1.603567451 + 1 = -0.603567451 y = -0.603567451 Simplifying y = -0.603567451Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.603567451, -0.603567451}
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