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# Solve the quadratic equation $\frac{1}{2}x^2+x+1=0$

## Step-by-step Solution

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### Videos

$x=-1+i,\:x=-1-i$
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## Step-by-step Solution

Problem to solve:

$\frac{1}{2} x^2+x+1=0$

Specify the solving method

1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=\frac{1}{2}$, $b=1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:

• $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=-1+\pm \sqrt{-1}$

Learn how to solve quadratic equations problems step by step online.

$x=-1+\pm \sqrt{-1}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 1/2x^2+x+1=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=\frac{1}{2}, b=1 and c=1. Then substitute the values of the coefficients of the equation in the quadratic formula:<ul><li>\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</li></ul>. Calculate the power \sqrt{-1} using complex numbers. As in the equation we have the sign \pm, this produces two identical equations that differ in the sign of the term i. We write and solve both equations, one taking the positive sign, and the other taking the negative sign.

$x=-1+i,\:x=-1-i$
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### beta Got another answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\frac{1}{2} x^2+x+1=0$