How do you solve using the completing the square method #x^2 + 6x = 7#?

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Answer 1 · 2017-07-20T16:02:28

#x=1 or -7#

#x^2+6x=7#

half the coefficient of #x# and square it

#6rarr3^2#

add and subtract this value

#color(red)(x^2+6x+3^2)-3^2=7#

#color(white)(==)uarr# the terms in red form a perfect square

#color(red)((x^2+6x+3^2))-9=7#

#color(white)(==)darr#

#=>color(red)((x+3)^2)=7+9#

#(x+3)^2=16#

now solve for #x#

#=>x+3=+-sqrt16#

#x+3=+-4#

#x=-3+-4#

#x=1 or -7#