Answer:
Two solutions were found :
x = 5
x = -5
Step-by-step explanation:
Step 1 :
Trying to factor as a Difference of Squares :
1.1 Factoring: 25-x2
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 : 25 is the square of 5
Check : x2 is the square of x1
Factorization is : (5 + x) • (5 - x)
Equation at the end of step 1 :
(x + 5) • (5 - x) = 0
Step 2 :
Theory - Roots of a product :
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
2.2 Solve : x+5 = 0
Subtract 5 from both sides of the equation :
x = -5
Solving a Single Variable Equation :
2.3 Solve : -x+5 = 0
Subtract 5 from both sides of the equation :
-x = -5
Multiply both sides of the equation by (-1) : x = 5
Two solutions were found :
x = 5
x = -5
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