Solve by Completing the Square 2x^2+11x-1=0

Problem

2*x2+11*x−1=0

Solution

1. Move the constant term to the right side of the equation by adding 1 to both sides.

2*x2+11*x=1

2. Divide by the leading coefficient to make the coefficient of x2 equal to 1

x2+11/2*x=1/2

3. Calculate the value to complete the square by taking half of the coefficient of x which is 11/4 and squaring it to get 121/16

(1/2⋅11/2)2=121/16

4. Add the calculated value to both sides of the equation.

x2+11/2*x+121/16=1/2+121/16

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

x2+11/2*x+121/16=8/16+121/16

x2+11/2*x+121/16=129/16

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

(x+11/4)2=129/16

7. Take the square root of both sides, remembering to include the plus-minus sign.

x+11/4=±√(,129/16)

x+11/4=±√(,129)/4

8. Isolate the variable by subtracting 11/4 from both sides.

x=−11/4±√(,129)/4

Final Answer

x=(−11±√(,129))/4

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