Problem 157 - College Algebra

Question

Explain how to solve \(x^{2}+6 x+8=0\) by completing the square.

Step-by-Step Solution

Answer

The solutions to the equation are \(x = -4\) and \(x = -2\).

Step 1: Identify a, b and c

From the equation \(x^2 + 6x + 8 = 0\), we can see that \(a = 1\), \(b = 6\) and \(c = 8\).

Step 2: Rearrange the equation

Remove the value of 'c' from the equation, which gives us \(x^2 + 6x = -8\). Then, add \((b/2a)^2\) to both sides of the equation, which is \((6/2*1)^2 = 9\). This gives us the equation \(x^2 + 6x + 9 = 1\).

Step 3: Complete the square

The left-hand side of the equation can now be written as a square, \((x + 3)^2\), which results in \((x + 3)^2 = 1\)

Step 4: Solve for x

Finally, we can solve for x by taking the square root of both sides. We obtain \(x + 3 = ±\sqrt{1}\). Therefore, \(x = -3 ± 1\), which gives \(x = -4\) and \(x = -2\)