Question

5. Solve (2x - 1)2 = 8 using the quadratic formula.

Answer 1

The solution to the equation by using quadratic formula is
`x = (1 + 2√(2))/(2) \ or \ (1 - 2√(2))/(2)`

Solving quadratic equation using formula.

Quadratic equation can be solved by using the quadratic formula
`x = (-b \pm √(b^2 -4ac))/(2a)`

The given equation (2x - 1)² = 8 can be written as 4x² - 4x - 7 = 0. where:

• a = 4
• b = -4
• c = -7

Replacing the values into the quadratic formula, we have:

`x = (-(-4) \pm √((-4)^2 -4(4)(-7)))/(2(4))`

`x = (4 \pm √(16 + 112))/(8)`

`x = (4 \pm √(128))/(8)`

`x = (4 \pm 8√(2))/(8)`

Divide the right hand side by 4;

`x = (1 \pm 2√(2))/(2)`

`x = (1 + 2√(2))/(2) \ or \ (1 - 2√(2))/(2)`

Answer 2

x= 4/10 or simplified to 2/5

Explanation:

multiply 2 by both (2x-1)= 4x-2=8

add 2 to both sides 4x=10

divide 4 from both sides x=4/10

simplify= 2/5