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

## Step-by-step Solution

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###  Videos

$x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}$
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##  Step-by-step Solution 

Problem to solve:

$x^2+x=5$

Specify the solving method

1

Rewrite the equation

$x^2+x-5=0$

Learn how to solve differential calculus problems step by step online.

$x^2+x-5=0$

Learn how to solve differential calculus problems step by step online. Solve the quadratic equation x^2+x=5. Rewrite the equation. 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=-5. 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 -5.

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

##  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

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

SnapXam A2

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5
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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:

Differential Calculus

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