Solving Quadratic Equation with Square Root
The equation provided in the image is:
√x - x = 0
To solve for x, start by isolating the square root term:
√x = x
Now, square both sides of the equation to eliminate the square root:
(√x)^2 = x^2
This simplifies to:
x = x^2
Rearrange the equation to set it to zero and find the values of x that satisfy the equation:
x^2 - x = 0
Factor x out of the expression:
x(x - 1) = 0
Now, set each factor equal to zero and solve for x:
x = 0
x - 1 = 0 => x = 1
The solutions are x = 0 and x = 1. However, you must check these solutions in the original equation because squaring both sides can introduce extraneous solutions.
For x = 0:
√0 - 0 = 0 => 0 = 0 (true)
For x = 1:
√1 - 1 = 0 => 1 - 1 = 0 (true)
Both solutions are valid, so x can be 0 or 1.
