Question

Solve 4u^(2)+8u=-1 by using the quadratic formula.

Answer 1

-1+
`√(3)`/2, -1-
`√(3)`/2

Explanation:

Quadratic formula= -b±
`\sqrt{b^(2)-4ac }` / 2a

4
`u^(2)`+8u=-1

add 1 to both sides

4
`u^(2)`+8u+1=0

a b c

label numbers with a,b,c

a=4

b=8

c=1

substitute into the quadratic formula

-b±
`\sqrt{b^(2)-4ac }` / 2a

-8±
`\sqrt{8^(2)-4(4)(1)` / 2(4)

solve

-8±
`\sqrt{8^(2)-4(4)(1)` / 2(4)

-8±
`√(64-16)` /8

-8±
`√(48)` /8

-8±4
`√(3)` /8

-8+4
`√(3)` /8, -8-4
`√(3)` /8

-1+
`√(3)`/2, -1-
`√(3)`/2

Answer 2

-1 + sqrt(3)/2 or -1 - sqrt(3)/2

Explanation:

First we rewrite the equation in the form of ax^2 + bx + c = 0.

Add 1 to both sides. 4u^2 + 8u + 1 = 0. Then we apply the quadratic formula -b plus minus root b^2 - 4ac all over 2a. Plug the values for a b and c in, and you should get your two possible answers - either -1 + sqrt(3)/2 or -1 - sqrt(3)/2.