How do you solve #x= sqrt(2x+3)#?
1 Answer
Explanation:
Right from the start, you know that you can only use positive values of
This means that you need to have
With this in mind, start by squaring both sides of the equation
#(sqrt(2x+3))^2 = x^2#
#2x + 3 = x^2#
Rearrange this equation by moving all the terms on one side
#x^2 - 2x - 3 = 0#
You can find the solutions to this quadratic equation by using the quadratic formula, which for a general form quadratic
#color(blue)(ax^2 + bx + c = 0)#
allows you to find the roots by using the formula
#color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a))#
In your case, you can write
#x_(1,2) = (-(-2) +- sqrt((-2)^2 - 4 * 1 * (-3)))/(2 * 1)#
#x_(1,2) = (2 +- sqrt(16))/2#
#x_(1,2) = (2 +- 4)/2 = {(x_1 = (2 + 4)/2 = 3), (x_2 = (2 - 4)/2 = -1) :}#
SInce
You can do a quick check to make sure that the calculations are correct
#sqrt(2 * 3 + 3) = 3#
#sqrt(9) = 3#
#3 = 3" "color(green)(sqrt())#