How do you solve (x - 2) ^ { 2} + 3= 4(x2)2+3=4?

2 Answers
Apr 28, 2018

x=3 and x=1x=3andx=1

Explanation:

first expand the quadratic equation
x^2-4x+4+3=4x24x+4+3=4
then sum all the unknown and the constant which will give you
x^2-4x+3=0x24x+3=0
then factorise the equation and u get
(x-3)(x-1)=0(x3)(x1)=0
therefore x=3 and x=1x=3andx=1

Apr 28, 2018

x=1" or "x=3x=1 or x=3

Explanation:

"isolate "(x-2)^2" by subtracting 3 from both sides"isolate (x2)2 by subtracting 3 from both sides

rArr(x-2)^2=4-3=1(x2)2=43=1

color(blue)"take the square root of both sides"take the square root of both sides

sqrt((x-2)^2)=+-sqrt1larrcolor(blue)"note plus or minus"(x2)2=±1note plus or minus

rArrx-2=+-1x2=±1

"add 2 to both sides"add 2 to both sides

rArrx=2+-1x=2±1

rArrx=2-1" or "x=2+1x=21 or x=2+1

rArrx=1" or "x=3x=1 or x=3