Question

Solve for x . √4x+5=x

Answer 1

subtract 5 from both sides

\[\sqrt{4x} = x - 5\]

next square both sides to remove the radical

\[4x = (x -5)^2\]

expand and simplify

\[4x = x^2 - 10x + 25\]

subtract 4x from both sides

\[x^2 - 14x + 25 = 0\]

use the general quadratic formula with a = 1, b = -14 and c = 25

\[x = \frac{14 \pm \sqrt{196 - 4 \times1\times25}}{2\times1}\]

\[x = \frac{14 \pm 4\sqrt{6}}{2} ... x = 7\pm2\sqrt{6}\]