What is the answer to ((x^{0.7}+7x)5+3)/4 =5 ?

The answer to ((x^{0.7}+7x)5+3)/4 =5 is x=0.40927…

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((x^{0.7}+7x)5+3)/4 =5

\frac{( x ^{0.7} + 7 x ) 5 + 3}{4} = 5

x = 0.40927 \dots

Solution steps

\frac{( x ^{0.7} + 7 x ) \cdot 5 + 3}{4} = 5

Multiply both sides by

4

\frac{( x ^{0.7} + 7 x ) \cdot 5 + 3}{4} \cdot 4 = 5 \cdot 4

Simplify

5 (x^{0.7} + 7 x) + 3 = 20

Expand

5 (x^{0.7} + 7 x) + 3 : 5 x^{0.7} + 35 x + 3

5 x^{0.7} + 35 x + 3 = 20

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{0.7} = (x^{\frac{1}{10}})^{(0.7 \cdot 10)}

5 (x^{\frac{1}{10}})^{7} + 35 (x^{\frac{1}{10}})^{10} + 3 = 20

Rewrite the equation with

x^{\frac{1}{10}} = u

5 u^{7} + 35 u^{10} + 3 = 20

Solve

5 u^{7} + 35 u^{10} + 3 = 20 : u \approx 0.91453 \dots, u \approx - 0.94758 \dots

u \approx 0.91453 \dots, u \approx - 0.94758 \dots

Substitute back

u = x^{\frac{1}{10}},

solve for

x

Solve

x^{\frac{1}{10}} = 0.91453 \dots : x = 0.40927 \dots

Solve

x^{\frac{1}{10}} = - 0.94758 \dots :

No Solution for

x \in R

x = 0.40927 \dots

Verify Solutions:

x = 0.40927 \dots

True

The solution is

x = 0.40927 \dots

c^{2} - 4 + 2 = c

9 x^{2} - 25 = 12

4 x - 3 x^{0.2} x = - 14

x^{2} - 3 3 x + 10 = 0

x + 2 x^{2} - 4 = 0

What is the answer to ((x^{0.7}+7x)5+3)/4 =5 ?
The answer to ((x^{0.7}+7x)5+3)/4 =5 is x=0.40927…
Solve for x: ((x^{0.7}+7x)5+3)/4 =5
The solution is x=0.40927…