Answer:
This problem has two number solutions. The solutions are x = ±√ 1.500 = ± 1.22474.
Step-by step explanation:
Step 1 :
Equation at the end of step 1 :
0 - ((0 - 2x2) + 3) = 0
Step 2 :
Trying to factor as a Difference of Squares :
2.1 Factoring: 2x2-3
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 : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step 2 :
2x2 - 3 = 0
Step 3 :
Solving a Single Variable Equation :
3.1 Solve : 2x2-3 = 0
Add 3 to both sides of the equation :
2x2 = 3
Divide both sides of the equation by 2:
x2 = 3/2 = 1.500
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 3/2
The equation has two real solutions
These solutions are x = ±√ 1.500 = ± 1.22474
