8b2-10b2+3=0
Two solutions were found :
b = ±√ 1.500 = ± 1.22474
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((8 • (b2)) - (2•5b2)) + 3 = 0
Step 2 :
Equation at the end of step 2 :
(23b2 - (2•5b2)) + 3 = 0
Step 3 :
Trying to factor as a Difference of Squares :
3.1 Factoring: 3-2b2
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 : 3 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step 3 :
3 - 2b2 = 0
Step 4 :
Solving a Single Variable Equation :
4.1 Solve : -2b2+3 = 0
Subtract 3 from both sides of the equation :
-2b2 = -3
Multiply both sides of the equation by (-1) : 2b2 = 3
Divide both sides of the equation by 2:
b2 = 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:
b = ± √ 3/2
The equation has two real solutions
These solutions are b = ±√ 1.500 = ± 1.22474
Two solutions were found :
b = ±√ 1.500 = ± 1.22474
