How to find the square root of 5x-25=0

x = ± √5 = ± 2.2361

Step-by-step explanation:

Two solutions were found:

x = ± √5 = ± 2.2361

Step by step solution:

Step 1:

Equation at the end of step 1:

5x2 - 25 = 0

Step 2:

Step 3:

Pulling out like terms:

3.1 Pull out like factors:

5x2 - 25 = 5 • (x2 - 5)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 5

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 3:

5 • (x2 - 5) = 0

Step 4:

Equations which are never true:

4.1 Solve : 5 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.2 Solve : x2-5 = 0

Add 5 to both sides of the equation:

x2 = 5

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 5

x = ± √5 = ± 2.2361