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# Solve the quadratic equation $x^2+x=5$

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##  Final answer to the problem

$x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
1

Factor the polynomial $x^2+x$. Add and subtract $\left(\frac{b}{2}\right)^2$, where in this case $b$ equals $1$

$x^2+x+\frac{1}{4}- \frac{1}{4}=5$

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

$x^2+x+\frac{1}{4}- \frac{1}{4}=5$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2+x=5. Factor the polynomial x^2+x. Add and subtract \left(\frac{b}{2}\right)^2, where in this case b equals 1. Now we can factor x^2+x+\frac{1}{4} as a squared binomial of the form \left(x+\frac{b}{2}\right)^2. Calculate the power \sqrt{\frac{1}{4}}. Multiply the fraction and term in - \frac{1}{4}.

##  Final answer to the problem

$x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}$

##  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

SnapXam A2

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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

###  Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.