# Equations » Square root equations

To solve square root equations follow these steps:

 1 Isolate the square root; so put the root form separate or use substitution as in example 3. 2 Square the left-hand side and the right-hand side of the equation. 3 Check whether the solutions of the squared equation are also solutions of the original equation.

Example 1 =  3x ( )2 = (3x)2 8x + 1 = 9x2 –9x2 + 8x + 1 = 0
 D = 82 – 4 · –9 · 1 = 100 x = –8 + 2 · –9 or x = –8 – 2 · –9 x = –19 or x = 1

Check:
Only x = 1 is a good solution when filling it in into the original equation.

Example 2

 2x – = 10 2x – 10 = (2x – 10)2 = ( )2 4x2 – 40x + 100 = x 4x2 – 41x + 100 = 0
 D = (–41)2 – 4 · 4 · –100 = 81 x = –(–41) + 2 · 4 or x = –(–41) – 2 · 4 x = 614 or x = 4

Check:
Only x = 614 is a good solution when filling it in into the original equation.

Example 3

 x5 – x2 · = 2 x5 – x2 · – 2 = 0 x5 – x2 · x0.5 – 2 = 0 x5 – x2.5 – 2 = 0 Substitute: p = x2.5 p2 – p – 2 = 0 (p + 1)(p – 2) = 0
 p = –1 or p = 2 x2.5 = –1 or x2.5 = 2 x = (–1)12.5 or x = 212.5 x = –1 or x ≈ 1.32

Check:
Only the solution x ≈ 1.32 is correct when used in the original equation.

Do you want an exact solution instead of x ≈ 1.32?

 x2.5 = 2 (x2.5)2 = 22 x5 = 4 x = To top