2b + 8 - 5B + 3 = - 13 + 8B - 5

Answer: b=2.4

Step-by-step explanation:

First you want to add the same things on the same side: 2b + (-5b) which equals - 3b

Then do the same thing to this:8+3=11

Then:-13-5=-18

Which shows as: 8-3b = - 18+8b

Then you take the smallest subscript: - 3b and add itself to itself: - 3b+3b=0

And do the same with the other subscript: 8b+3b=11b

Which shows as: 8=-18+11b

Then box the 11b and add the - 18 to itself: - 18+18=0

Do the same with the other side: 8+18=26

Which shows as: 26=11b

Then divide each side by 11.

Then this is your answer: b=2.4

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