Solve by Completing the Square x^2+8x+9=0

Problem

x2+8*x+9=0

Solution

1. Isolate the constant term by subtracting 9 from both sides of the equation.

x2+8*x=−9

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it: (8/2)2=4=16

(8/2)2=16

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

x2+8*x+16=−9+16

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

(x+4)2=7

5. Apply the square root property by taking the square root of both sides, remembering to include the plus-minus sign.

x+4=±√(,7)

6. Solve for x by subtracting 4 from both sides.

x=−4±√(,7)

Final Answer

x=−4±√(,7)

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