Solve by Completing the Square x^2+5x-9=0

Problem

x^2+5*x−9=0

Solution

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

x^2+5*x=9

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it.

Value=(5/2)^2

Value=25/4

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

x^2+5*x+25/4=9+25/4

4. Factor the left side as a perfect square trinomial and simplify the right side using a common denominator.

(x+5/2)^2=36/4+25/4

(x+5/2)^2=61/4

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

x+5/2=±√(,61/4)

x+5/2=±√(,61)/2

6. Isolate x by subtracting 5/2 from both sides.

x=−5/2±√(,61)/2

Final Answer

x=(−5±√(,61))/2

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