Question - Solving Quadratic Equation with Square Root
mathsolving quadratic equationsquare root methodisolating square root termquadratic equation solutions
Solution:
The equation provided in the image is:√x - x = 0To solve for x, start by isolating the square root term:√x = xNow, square both sides of the equation to eliminate the square root:(√x)^2 = x^2This simplifies to:x = x^2Rearrange the equation to set it to zero and find the values of x that satisfy the equation:x^2 - x = 0Factor x out of the expression:x(x - 1) = 0Now, set each factor equal to zero and solve for x:x = 0x - 1 = 0 => x = 1The 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.
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