Question

What are the solutions of 2x2 + 16x + 34 = 0?

–8 ± 2i

–8 ± i

–4 ± 2i

–4 ± i

Answer 1

`\text{The solution is }x=-4\pm i`

Explanation:

Given the equation

`2x^2+16x+34=0`

we have to find the solutions of above equation

`2x^2+16x+34=0`

Comparing it with standard quadratic equation
`ax^2+bx+c=0`

a=2, b=16, c=34

The solution is

`x=(-b\pm √(b^2-4ac))/(2a)`

`x=(-16\pm √(16^2-4(2)(34)))/(2(2))`

`x=(-16\pm √(-16))/(4)`

`x=-4\pm i`

`\text{The solution is }x=-4\pm i`

Answer 2

2x^2 + 16x + 34 = 0
x^2 + 8x + 17 = 0
x^2 + 8x + 16 = -17 + 16 = -1
(x + 4)^2 = -1
x + 4 = sqrt(-1) = ±i
x = -4 ± i