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Solve the exponential equation $2^{2x}+2^x-56=0$

Step-by-step Solution

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Final answer to the problem

$x=2.8073549$
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Step-by-step Solution

How should I solve this problem?

  • Factor by completing the square
  • Solve for x
  • Find the roots
  • Solve by factoring
  • Solve by completing the square
  • Solve by quadratic formula (general formula)
  • Find break even points
  • Find the discriminant
  • Exact Differential Equation
  • Linear Differential Equation
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1

Rewriting the exponent $2^{2x}$

$\left(2^x\right)^2+2^x-56=0$

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

$\left(2^x\right)^2+2^x-56=0$

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Learn how to solve implicit differentiation problems step by step online. Solve the exponential equation 2^(2x)+2^x+-56=0. Rewriting the exponent 2^{2x}. We can try to factor the expression \left(2^x\right)^2+2^x-56 by applying the following substitution. Substituting in the polynomial, the expression results in. Factor the trinomial u^2+u-56 finding two numbers that multiply to form -56 and added form 1.

Final answer to the problem

$x=2.8073549$

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Function Plot

Plotting: $2^{2x}+2^x-56$

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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

How to improve your answer:

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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