How do you solve #x^2+8x=20# using completing the square?

Question

Hazel Anglin · Accepted Answer

#(x+4)^2-16=20# #(x+4)^2=36# both sides' square root #x+4=\pm6# #x+4=6 or x+4=-6# #x=2 or x=-10#

Nathan Axel · Answer

#x=2# and #x=-10#

When we complete the square, we want to take half of our #b# value, square it, and add it to the left side. Doing this, we get

#x^2+8x+color(blue)(16)=20+color(blue)(16)#

#16# is the value #(8/2)^2#. Notice, we add it to both sides to maintain the equality.

We can further simplify our equation as

#(x+4)^2=36#

By taking both sides' square roots, we arrive at

#x+4=6# and #x+4=-6#

When we solve these equations, we get

#x=2# and #x=-10#

I hope this is useful.

Isaiah Anthony · Answer

undefined To solve the equation x^2 + 8x = 20 using completing the square:

1. Move the constant term to the other side to isolate the terms involving x:
   x^2 + 8x - 20 = 0

2. Add and subtract the square of half the coefficient of x (8/2)^2 = 16 to both sides of the equation:
   x^2 + 8x + 16 - 16 - 20 = 0

3. Rewrite the left side as a perfect square trinomial:
   (x + 4)^2 - 36 = 0

4. Add 36 to both sides to isolate the squared term:
   (x + 4)^2 = 36

5. Take the square root of both sides and solve for x:
   x + 4 = ±√36
   x + 4 = ±6
   x = -4 ± 6

6. Solve for x:
   x = -4 + 6 or x = -4 - 6
   x = 2 or x = -10

Therefore, the solutions to the equation x^2 + 8x = 20 are x = 2 and x = -10.