Use completing the square to solve. Show solution please ☺️

Question

8x²-10x-3=0

Answer 1

8x²-10x-3=0

 

Step 1:  Divide through by 8 to get the leading coefficient equal to 1

 

x² - (10/8)x - 3/8 = 0

x² - (5/4) - 3/8 = 0

 

Step 2:  Add 3/8 to both sides

 

x² - (5/4)x = 3/8

 

Step 3:

Take 1/2 of the coefficient of x, square it, add that to both sides:

(1/2)(-5/4) = -5/8 ... (-5/8)² = 25/64

 

x² - (5/4)x + 25/64 = 3/8 + 25/64

x² - (5/4)x + 25/64 = 49/64

 

Step 4:  Change the left side to the equivalent square term:

The left side is now equivalent to (x-5/8)² so:

 

(x - 5/8)² = 49/64

 

Step 5:  Take square root of both sides:

 

x- 5/8 = ± √(49/64)

x- 5/8 = ± 7/8

 

Step 6:  Add the constant to both sides:

x = 5/8 ± 7/8

x = (5 ± 7)/8

 

x = 12/8 = 3/2

or

x = -2/8 = -1/4

 

Check Answer:

8x²-10x-3=0

 

8(3/2)² - 10(3/2) - 3 = 0

8(9/4) - 15 - 3 = 0

18 - 15 - 3 = 0

0 = 0   

Answer x = 3/2 checks

 

8(-1/4)² - 10(-1/4) - 3 = 0

8(1/16) + 10/4 - 3 = 0

1/2 + 2 1/2 - 3 = 0

3 - 3 = 0

0 = 0

Answer x = =1/4 checks