how to solve

Question

√3x+13=x-5

Answer 1

√(3x) + 13 = x - 5

 

√(3x) = x - 18

 

Square both sides

 

3x = x^2 - 36x + 324

 

x^2 - 39x + 324 = 0

 

(x - 12)(x - 27) = 0

 

x = 12, 27

 

check:

 

√(3(12)) + 13 =? (12) - 5

6 + 13 =? (12) - 5
18 ≠ 7 so 12 is not a solution; it's extraneous.

 

√(3(27)) + 13 =? (27) - 5

9 + 13 = 22 √

The only solution is x = 27.

Answer 2

Hi, Mondrea!

 

This equation could be solved a few different ways, depending on what is underneath the square root sign on the left side of the equation.  In this solution, I assumed that the entire left side of the equation is under the square root symbol.

 

√(3x+13) = x-5

 

1. Square both sides of the equation to remove the square root symbol:

[√(3x+13)]² = [x-5]²

3x+13 = (x-5)(x-5)

 

2. Use FOIL to multiply the two binomials on the right side.  Then move the terms on the left of the equation to the right side so that the x² part of the equation is equal to zero.

3x+13 = x²-10x+25

-3x            -3x

13 = x²-13x+25

-13            -13

0 = x²-13x+12

 

3. Now factor the right side of the equation.  Set each binomial equal to zero and solve for x.

0 = x²-13x+12

0 = (x-12)(x-1)

x-12 = 0     x-1 = 0

    x = 12       x = 1

 

4. Check to make sure that both answers work in the original equation.

x = 12

√(3x+13) = x-5

√(3*12+13) = 12-5

√(36+13) = 7

√49 = 7

7 = 7

 

x = 1

√(3*1+13) = 1-5

√(3+13) = -4

√16 = -4  NO - so we reject the answer x = 1.

 

Solution: x = 12.

 

Hope this helps!

 

Patty