Question

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot
8(x2 + 2x + 1) = 3 + 1
8(x2 + 2x) = –3

Answer 1

1

2

5

Explanation:

Answer 2

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Explanation:

Solving Quadratic Equations

Sometimes it's preferred to solve quadratic equations without the use of the known quadratic formula solver. One of the most-used methods consists of completing squares and solving for x.

We have the equation

`\displaystyle 8x^2+16x+3=0`

We separate variables from constants

`\displaystyle 8x^2+16x=-3`

Taking the common factor 8

`\displaystyle 8(x^2+2x)=-3`

Completing squares in the brackets and balancing the equation in the right side

`\displaystyle 8(x^2+2x+1)=-3+8`

Factoring the perfect square

`\displaystyle 8(x+1)^2=5`

Isolating x

`\displaystyle (x+1)^2=(5)/(8)`

`\displaystyle (x+1)=\pm \sqrt{(5)/(8)}`

`\displaystyle x=-1\pm \sqrt{(5)/(8)}`

We can clearly see the steps used to solve the quadratic equation are (in order and written like in the question)

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot