Question

Solve each equation using the quadratic formula. Find the exact solution, then approximate the solution to the nearest hundredth.

8x^2 - 8x + 2 = 0

Needs to be answered like this:

Answer 1

x= 0.5

Explanation:

given equation is :

8x²-8x+2 =0

ax²+bx+c = 0 is general quadratic equation.

x =(-b±√b²-4ac) / 2a is solution of general equation.

compare general equation with given quadratic equation,we get

a = 8, b = -8 and c = 2

putting above values in quadratic formula,we get

x = (-(-8)±√(-8)²-4(8)(2)) / 2(8)

x= (8±√64-64) / 16

x= (8±√0) / 16

x = (8±0) / 16

x = 8+0/ 16 or x= 8-0/ 16

x= 8/16 or 8/16

x = 1/2 or 1/2

x= 0.5

hence, the solution of 8x²-8x+2=0 is {0.5}.

Answer 2

`x_1=x_2=0.5.`

Explanation:

The equation
`8x^2-8x+2=0` is quadratic equation with
`a=8,\ b=-8, c=2`. Find the discriminant:

`D=b^2-4ac=(-8)^2-4\cdot 8\cdot 2=64-64=0.`

Then the exast solutions of the equation are

`x_1=(-b-√(D))/(2a)=(-(-8)-√(0))/(2\cdot 8)=(8-0)/(16)=(1)/(2),\\ \\x_2=(-b+√(D))/(2a)=(-(-8)+√(0))/(2\cdot 8)=(8+0)/(16)=(1)/(2).`

The solutions are:

`x_1=x_2=0.5.`