Solve by Completing the Square 2y^2+10y=-7

Problem

2*y2+10*y=−7

Solution

1. Divide the entire equation by the leading coefficient 2 to ensure the y2 term has a coefficient of 1

y2+5*y=−7/2

2. Identify the coefficient of the linear term y which is 5

3. Calculate the value needed to complete the square by taking half of the linear coefficient and squaring it: (5/2)2=25/4

4. Add 25/4 to both sides of the equation to maintain equality.

y2+5*y+25/4=−7/2+25/4

5. Simplify the right side by finding a common denominator.

−7/2+25/4=−14/4+25/4=11/4

6. Factor the left side as a perfect square trinomial.

(y+5/2)2=11/4

7. Take the square root of both sides, remembering to include both the positive and negative roots.

y+5/2=±√(,11/4)

8. Simplify the radical on the right side.

y+5/2=±√(,11)/2

9. Isolate y by subtracting 5/2 from both sides.

y=−5/2±√(,11)/2

Final Answer

y=(−5±√(,11))/2

Want more problems? Check here!