How do you solve (x+1)^2-9/4=0?

3 Answers
Alan P.
Feb 6, 2017

x=-5/2color(white)("XX")orcolor(white)("XX")x=+1/2

Explanation:

(x+1)^2-9/4=0

rarr (x+1)^2 = 9/4

rarr x+1 = +-3/2

rarr x=-1+-3/2

rarr x=-5/2color(white)("XX")orcolor(white)("XX")x=+1/2

Dwight
Feb 6, 2017

Being a second-order equation, their are two solutions

x=1/2 and x=-5/2

Explanation:

First, move the right-most term to the right side of the equation

(x+1)^2=9/4

Now, take the square root of each side. Don't forget that there will be two roots to the right side:

x+1=+-3/2

So, the answers are

x=+3/2-1 or x=1/2
and

x=-3/2-1 or x=-5/2

EZ as pi
Feb 6, 2017

x = -2 1/2 " or " x = 1/2

Explanation:

While you could multiply out the bracket and then simplify and factorise the quadratic trinomial, an easier method is to realize that

(x+1)^2-9/4 can be factorised as the difference of squares.

x^2 -y^2 = (x+y)(x-y)

So, if (x+1)^2-9/4 = 0

then (x+1+3/2)(x+1-3/2)=0

Consider each factor being equal to 0.

x+1+3/2 = 0" "rarr x = -5/2 = -2 1/2

x+1 -3/2 =0" "rarr x = 1/2

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