Question

What value completes the square for the expression? x2 + 14x

Use the quadratic formula to solve the equation. x2 – 7x – 6 = 0

Simplify the expression. (–2i)(8i)

What are the solutions?
1/2x^2 + 2x + 3 =0

I need help

Answer 1

for number one we see that this could be of the form (x+7)^2 so we expand to get x^2+14x+49 so we need to add 49

for number 2 we can just use the easy way (factoring) although you can use the quad formula. (x-1)(x-6) to get x=1,6

we multiply coefficients pretending i is a variable. so we get -16 i^2. we know i is the square root of -1 so i^2 = -1. Thus -16 i^2 = 16.

for the last one, multiply both sides by 2x^2 to get 1+2x^3+6x^2. Then we can let y=x^2. Thus we get 1+2y^2+6y and we rearrange terms to get 2y^2+6y+1.

through the quadratic formula etc. we get a complicated non-real answer: x= (-4+2i\sqrt2)/2, (-4-2i\sqrt2)/2