Solve by Completing the Square 2y^2+10y=-9

Problem

2*y2+10*y=−9

Solution

1. Divide the entire equation by the leading coefficient 2 to make the y2 coefficient equal to 1

(2*y2+10*y)/2=(−9)/2

y2+5*y=−4.5

2. Identify the coefficient of the linear term, which is 5 and calculate the value needed to complete the square by squaring half of it.

(5/2)2=25/4=6.25

3. Add 6.25 to both sides of the equation to maintain equality.

y2+5*y+6.25=−4.5+6.25

y2+5*y+6.25=1.75

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

(y+2.5)2=1.75

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

y+2.5=±√(,1.75)

6. Isolate y by subtracting 2.5 from both sides.

y=−2.5±√(,1.75)

7. Simplify the radical expression if possible. Note that 1.75=7/4

√(,1.75)=√(,7/4)=√(,7)/2

y=−5/2±√(,7)/2

Final Answer

y=(−5±√(,7))/2

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