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# Solve the quadratic equation $\frac{1}{4}+x^2+x+1=0$

## Step-by-step Solution

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$x=\frac{-1+2i}{2},\:x=\frac{-1-2i}{2}$
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##  Step-by-step Solution 

Problem to solve:

$\frac{1}{4}+x^2+x+1=0$

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1

Add the values $\frac{1}{4}$ and $1$

$\frac{5}{4}+x^2+x=0$

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

$\frac{5}{4}+x^2+x=0$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 1/4+x^2x+1=0. Add the values \frac{1}{4} and 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=1, b=1 and c=\frac{5}{4}. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Multiply -4 times \frac{5}{4}.

$x=\frac{-1+2i}{2},\:x=\frac{-1-2i}{2}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even pointsFind the discriminant

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7
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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

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