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

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Jun 19, 2018

Answer:

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

Explanation:

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.

Our equation can be further simplified as

#(x+4)^2=36#

Taking the square root of both sides, we get

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

Solving these equations gives us

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

Hope this helps!

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Mark D. Share
Jun 19, 2018

#(x+4)^2-16=20#

#(x+4)^2=36#

Square root both sides

#x+4=\pm6#

#x+4=6 or x+4=-6#

#x=2 or x=-10#

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