How do you complete the square to solve x^2+6x=7x2+6x=7?

1 Answer
Don't Memorise
May 31, 2015

x^2 + 6x = 7x2+6x=7
To write the Left Hand Side as a Perfect Square, we add 9 to both sides
x^2 + 6x + 9= 7+ 9x2+6x+9=7+9
x^2 + 2*3*x + 3^2 = 16x2+2⋅3⋅x+32=16
Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2, we get
(x+3)^2 = 16(x+3)2=16
x + 3 = +sqrt16x+3=+√16 or x +3 = -sqrt16x+3=−√16
x =4-3or x = -4 - 3x=4−3orx=−4−3
color(green)(x = 1 or color(green)(x = -7x=1orx=−7

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