Solve by Completing the Square x^2+4x-9=0

Problem

x2+4*x−9=0

Solution

1. Move the constant term to the right side of the equation by adding 9 to both sides.

x2+4*x=9

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

(4/2)2=4

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

x2+4*x+4=9+4

4. Factor the perfect square trinomial on the left side and simplify the right side.

(x+2)2=13

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

x+2=±√(,13)

6. Isolate the variable x by subtracting 2 from both sides.

x=−2±√(,13)

Final Answer

x=−2±√(,13)

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