Answer:
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