How do you use the square root property to solve this equation #(2x+3)^2 = 25#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Don't Memorise
Aug 13, 2015

The solutions are
#color(blue)(x=1,x=-4#

Explanation:

The square root property involves taking the square root of both the terms on either side of the equation.

Applying the same to the given equation:

#sqrt((2x+3)^2)=sqrt(25#

(#sqrt25= color(blue)(+-5#)

So,
#sqrt((2x+3)^2)=color(blue)(+-5#

#(2x+3)=color(blue)(+-5#

Solution 1:
#2x+3 = +5#
Isolating #x#
#2x+3 -color(blue)(3)= +5-color(blue)(3)#
#2x=2#
#color(blue)(x=1#

Solution 2:
#2x+3 = -5#
Isolating #x#
#2x+3 -color(blue)(3)= -5-color(blue)(3)#
#2x=-8#
#color(blue)(x=-4#

Related questions
See all questions in Use Square Roots to Solve Quadratic Equations
Impact of this question
7158 views around the world
You can reuse this answer
Creative Commons License