Solve by Completing the Square x^2+6x+8=0

Problem

x2+6*x+8=0

Solution

1. Isolate the constant term by subtracting 8 from both sides of the equation.

x2+6*x=−8

2. Calculate the value to complete the square by taking half of the coefficient of x which is 6 and squaring it.

6/2=3

3=9

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

x2+6*x+9=−8+9

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

(x+3)2=1

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

x+3=±√(,1)

x+3=±1

6. Solve for x by subtracting 3 from both sides for both cases.

x=−3+1⇒x=−2

x=−3−1⇒x=−4

Final Answer

x={−4,−2}

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