Answer:
x = ± √5 = ± 2.2361
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