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Find the roots of $\left(3+2\sqrt{2}\right)x^2-2\sqrt{2}\cdot \left(\sqrt{2}+1\right)x+2=0$

Step-by-step Solution

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Final answer to the problem

$x=\frac{6.828427}{11.6568542}$
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Step-by-step Solution

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The product of powers of the same base is equal to the base raised to the sum of the exponents: $a^m\cdot a^n=a^{m+n}$

$\left(3+2^{\left(\frac{1}{2}+1\right)}\right)x^2-2\sqrt{2}\cdot \left(\sqrt{2}+1\right)x+2=0$

Learn how to solve definition of derivative problems step by step online.

$\left(3+2^{\left(\frac{1}{2}+1\right)}\right)x^2-2\sqrt{2}\cdot \left(\sqrt{2}+1\right)x+2=0$

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Learn how to solve definition of derivative problems step by step online. Find the roots of (3+22^1/2)x^2-22^1/2(2^1/2+1)x+2=0. The product of powers of the same base is equal to the base raised to the sum of the exponents: a^m\cdot a^n=a^{m+n}. Add the values \frac{1}{2} and 1. Multiply the single term x^2 by each term of the polynomial \left(3+\sqrt{\left(2\right)^{3}}\right). Multiply the single term -2\sqrt{2}x by each term of the polynomial \left(\sqrt{2}+1\right).

Final answer to the problem

$x=\frac{6.828427}{11.6568542}$

Exact Numeric Answer

$x=0.5858$

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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 xSolve by factoringSolve by completing the squareSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Plotting: $\left(3+2\sqrt{2}\right)x^2-2\sqrt{2}\cdot \left(\sqrt{2}+1\right)x+2$

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7
8
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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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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