Question

Solve the equation x^2 = 26 ​

Answer 1

x = ± √26 = ± 5.0990

Explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(26)=0

Step by step solution :

STEP

1

:

Trying to factor as a Difference of Squares:

1.1 Factoring: x2-26

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 : 26 is not a square !!

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

Equation at the end of step

1

:

x2 - 26 = 0

STEP

2

:

Solving a Single Variable Equation:

2.1 Solve : x2-26 = 0

Add 26 to both sides of the equation :

x2 = 26

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

x = ± √ 26

The equation has two real solutions

These solutions are x = ± √26 = ± 5.0990

Answer 2

x=±
`√(26)`

Explanation:

1 - Rewrite

`x^2 = 26`

2 - Square root both sides to get the value of just x alone

`√(x^2) = √(26)`

3 - Give 26 a ± and simplify

`x=` ±
`√(26)`