Question
Solve the equation
x1=−656480,x2=656480
Alternative Form
x1≈−0.964193,x2≈0.964193
Evaluate
∣2x×1∣3x4=5
Simplify
More Steps

Evaluate
∣2x×1∣3x4
Multiply the terms
∣2x∣3x4
When the expression in absolute value bars is not negative, remove the bars
∣2x∣×3x4
Any expression multiplied by 1 remains the same
3x4∣2x∣
3x4∣2x∣=5
Separate the equation into 2 possible cases
3x4×2x=5,2x≥03x4(−2x)=5,2x<0
Evaluate
More Steps

Evaluate
3x4×2x=5
Calculate
6x4×x=5
Expand the expression
More Steps

Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
6x5=5
Divide both sides
66x5=65
Divide the numbers
x5=65
Take the 5-th root on both sides of the equation
5x5=565
Calculate
x=565
Simplify the root
More Steps

Evaluate
565
To take a root of a fraction,take the root of the numerator and denominator separately
5655
Multiply by the Conjugate
56×56455×564
Simplify
56×56455×51296
Multiply the numbers
56×56456480
Multiply the numbers
656480
x=656480
x=656480,2x≥03x4(−2x)=5,2x<0
Evaluate
x=656480,x≥03x4(−2x)=5,2x<0
Evaluate
More Steps

Evaluate
3x4(−2x)=5
Calculate
−6x4×x=5
Expand the expression
More Steps

Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
−6x5=5
Change the signs on both sides of the equation
6x5=−5
Divide both sides
66x5=6−5
Divide the numbers
x5=6−5
Use b−a=−ba=−ba to rewrite the fraction
x5=−65
Take the 5-th root on both sides of the equation
5x5=5−65
Calculate
x=5−65
Simplify the root
More Steps

Evaluate
5−65
An odd root of a negative radicand is always a negative
−565
To take a root of a fraction,take the root of the numerator and denominator separately
−5655
Multiply by the Conjugate
56×564−55×564
Simplify
56×564−55×51296
Multiply the numbers
56×564−56480
Multiply the numbers
6−56480
Calculate
−656480
x=−656480
x=656480,x≥0x=−656480,2x<0
Evaluate
x=656480,x≥0x=−656480,x<0
Find the intersection
x=656480x=−656480,x<0
Find the intersection
x=656480x=−656480
Solution
x1=−656480,x2=656480
Alternative Form
x1≈−0.964193,x2≈0.964193
Show Solution
