What is the answer to x^{2.6}x-3.5=4.2x+1.2 ?

The answer to x^{2.6}x-3.5=4.2x+1.2 is x=-0.93332…,x=2.05298…

Solve for x: x^{2.6}x-3.5=4.2x+1.2

The solution is x=-0.93332…,x=2.05298…

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x^{2.6} x - 3.5 = 4.2 x + 1.2

x = - 0.93332 \dots, x = 2.05298 \dots

Solution steps

x^{2.6} x - 3.5 = 4.2 x + 1.2

Use the following exponent property

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

x^{2.6} = (x^{\frac{1}{5}})^{(2.6 \cdot 5)}

(x^{\frac{1}{5}})^{13} (x^{\frac{1}{5}})^{5} - 3.5 = 4.2 (x^{\frac{1}{5}})^{5} + 1.2

Rewrite the equation with

x^{\frac{1}{5}} = u

u^{13} u^{5} - 3.5 = 4.2 u^{5} + 1.2

Solve

u^{13} u^{5} - 3.5 = 4.2 u^{5} + 1.2 : u \approx - 0.98629 \dots, u \approx 1.15472 \dots

u \approx - 0.98629 \dots, u \approx 1.15472 \dots

Substitute back

u = x^{\frac{1}{5}},

solve for

x

Solve

x^{\frac{1}{5}} = - 0.98629 \dots : x = - 0.93332 \dots

Solve

x^{\frac{1}{5}} = 1.15472 \dots : x = 2.05298 \dots

x = - 0.93332 \dots, x = 2.05298 \dots

Verify Solutions:

x = - 0.93332 \dots

True

, x = 2.05298 \dots

True

The solutions are

x = - 0.93332 \dots, x = 2.05298 \dots

n (x - 3) = (x - 3) - 3

x - 2 x - 1 = 0

a - 5 = 10

3 x^{2} + 2 = 0

What is the answer to x^{2.6}x-3.5=4.2x+1.2 ?
The answer to x^{2.6}x-3.5=4.2x+1.2 is x=-0.93332…,x=2.05298…
Solve for x: x^{2.6}x-3.5=4.2x+1.2
The solution is x=-0.93332…,x=2.05298…