Answer:
x = ± √7 = ± 2.6458
Explanation:
Step 1 :
Equation at the end of step 1 :
7x2 - 49 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
7x2 - 49 = 7 • (x2 - 7)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 7
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 : 7 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
7 • (x2 - 7) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 7 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x2-7 = 0
Add 7 to both sides of the equation :
x2 = 7
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 7
The equation has two real solutions
These solutions are x = ± √7 = ± 2.6458