Answer:
2
:
5STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 5-3x2
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
2
:
5 - 3x2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : -3x2+5 = 0
Subtract 5 from both sides of the equation :
-3x2 = -5
Multiply both sides of the equation by (-1) : 3x2 = 5
Divide both sides of the equation by 3:
x2 = 5/3 = 1.667
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 5/3
The equation has two real solutions
These solutions are x = ±√ 1.667 = ± 1.29099
Two solutions were found :
x = ±√ 1.667 = ± 1.29099