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Find the break even points of the expression $2x^2+x^2=-1\cdot 1^2+x^2$

Step-by-step Solution

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Solution

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Final Answer

$x=\frac{\sqrt{2}}{2}i,\:x=-\frac{\sqrt{2}}{2}i$
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Step-by-step Solution

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Combining like terms $2x^2$ and $x^2$

$3x^2=-1\cdot 1^2+x^2$

Learn how to solve implicit differentiation problems step by step online.

$3x^2=-1\cdot 1^2+x^2$

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Learn how to solve implicit differentiation problems step by step online. Find the break even points of the expression 2x^2+x^2=-1^2+x^2. Combining like terms 2x^2 and x^2. Calculate the power 1^2. Rearrange the equation. Grouping all terms to the left side of the equation.

Final Answer

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

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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 formula (general formula)Find the discriminant

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Function Plot

Plotting: $2x^2+x^2+1^2-x^2$

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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
D□x
∫
∫◻
|◻|
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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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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