Question
Solve the equation
x=−5746875
Alternative Form
x≈−0.929624
Evaluate
x÷5x−2=3x6×x
Find the domain
More Steps

Evaluate
5x=0
Rewrite the expression
x=0
x÷5x−2=3x6×x,x=0
Simplify
More Steps

Evaluate
x÷5x−2
Divide the terms
More Steps

Evaluate
x÷5x
Rewrite the expression
5xx
Reduce the fraction
51
51−2
Reduce fractions to a common denominator
51−52×5
Write all numerators above the common denominator
51−2×5
Multiply the numbers
51−10
Subtract the numbers
5−9
Use b−a=−ba=−ba to rewrite the fraction
−59
−59=3x6×x
Multiply
More Steps

Evaluate
3x6×x
Multiply the terms with the same base by adding their exponents
3x6+1
Add the numbers
3x7
−59=3x7
Swap the sides of the equation
3x7=−59
Multiply by the reciprocal
3x7×31=−59×31
Multiply
x7=−59×31
Multiply
More Steps

Evaluate
−59×31
Reduce the numbers
−53×1
Multiply the numbers
−53
x7=−53
Take the 7-th root on both sides of the equation
7x7=7−53
Calculate
x=7−53
Simplify the root
More Steps

Evaluate
7−53
An odd root of a negative radicand is always a negative
−753
To take a root of a fraction,take the root of the numerator and denominator separately
−7573
Multiply by the Conjugate
75×756−73×756
Simplify
75×756−73×715625
Multiply the numbers
More Steps

Evaluate
−73×715625
The product of roots with the same index is equal to the root of the product
−73×15625
Calculate the product
−746875
75×756−746875
Multiply the numbers
More Steps

Evaluate
75×756
The product of roots with the same index is equal to the root of the product
75×56
Calculate the product
757
Reduce the index of the radical and exponent with 7
5
5−746875
Calculate
−5746875
x=−5746875
Check if the solution is in the defined range
x=−5746875,x=0
Solution
x=−5746875
Alternative Form
x≈−0.929624
Show Solution
