Final answer:
To solve √(2x+3) = x, we square both sides to get a quadratic equation, solve it using the quadratic formula, and then verify the solutions to discard any extraneous ones.
Step-by-step explanation:
To solve the equation √(2x+3) = x, we will first square both sides to remove the square root:
x^2 = 2x + 3
Next, rearrange the equation to set it to zero:
x^2 - 2x - 3 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To find the solution, we apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values we get:
a = 1, b = -2, c = -3
x = (2 ± √(4 + 12)) / 2
x = (2 ± √16) / 2
x = (2 ± 4) / 2
Which gives us two possible solutions for x:
x = (2 + 4) / 2 -> x = 3
x = (2 - 4) / 2 -> x = -1
However, we must verify these solutions by substituting back into the original equation because squaring both sides can introduce extraneous solutions.