Question
what is the solution to x= sqrt. 2x+3
a) 3
b) -1
c) 3 and -1
d)-3 and 1
a) 3
b) -1
c) 3 and -1
d)-3 and 1
Answers
GPT 3.5
To find the solution to the equation x = √(2x + 3), we need to isolate x on one side of the equation. Here's how we can do that:
x = √(2x + 3)
Squaring both sides of the equation to eliminate the square root:
x^2 = 2x + 3
Moving all terms to one side of the equation:
x^2 - 2x - 3 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Factoring is the most efficient method here:
(x - 3)(x + 1) = 0
Setting each factor equal to 0 and solving for x:
x - 3 = 0, so x = 3
x + 1 = 0, so x = -1
Therefore, the solution to the equation x = √(2x + 3) is:
x = 3 and x = -1
So, the answer is c) 3 and -1.
x = √(2x + 3)
Squaring both sides of the equation to eliminate the square root:
x^2 = 2x + 3
Moving all terms to one side of the equation:
x^2 - 2x - 3 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Factoring is the most efficient method here:
(x - 3)(x + 1) = 0
Setting each factor equal to 0 and solving for x:
x - 3 = 0, so x = 3
x + 1 = 0, so x = -1
Therefore, the solution to the equation x = √(2x + 3) is:
x = 3 and x = -1
So, the answer is c) 3 and -1.