Answer:
x=2
x=-2
Explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-3-(1)=0
1.1 Factoring: x2-4
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 : 4 is the square of 2
Check : x2 is the square of x1
Factorization is : (x + 2) • (x - 2)
Equation at the end of step
1
:
(x + 2) • (x - 2) = 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+2 = 0
Subtract 2 from both sides of the equation :
x = -2
Solving a Single Variable Equation:
2.3 Solve : x-2 = 0
Add 2 to both sides of the equation :
x = 2