Solve by Completing the Square 2x^2+9x-1=0

Problem

2*x2+9*x−1=0

Solution

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

2*x2+9*x=1

2. Divide by the leading coefficient to ensure the x2 term has a coefficient of 1.

x2+9/2*x=1/2

3. Find the value to complete the square by taking half of the x coefficient and squaring it: (1/2⋅9/2)2=(9/4)2=81/16

Value=81/16

4. Add the value to both sides of the equation to maintain equality.

x2+9/2*x+81/16=1/2+81/16

5. Simplify the right side by finding a common denominator: 1/2=8/16

x2+9/2*x+81/16=89/16

6. Factor the perfect square trinomial on the left side.

(x+9/4)2=89/16

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

x+9/4=±√(,89)/4

8. Isolate the variable by subtracting 9/4 from both sides.

x=−9/4±√(,89)/4

Final Answer

x=(−9±√(,89))/4

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