Solve 45-1604040 a^4

Question

Factor the expression

15 (3 - 106936 a^{4})

Evaluate

45 - 1604040 a^{4}

Solution

15 (3 - 106936 a^{4})

Show Solution

a_{1} = - \frac{4 3 \times 10693 6 ^{3}}{106936}, a_{2} = \frac{4 3 \times 10693 6 ^{3}}{106936}

Alternative Form

a_{1} \approx - 0.072778, a_{2} \approx 0.072778

Evaluate

45 - 1604040 a^{4}

To find the roots of the expression,set the expression equal to 0

45 - 1604040 a^{4} = 0

Move the constant to the right-hand side and change its sign

- 1604040 a^{4} = 0 - 45

Removing 0 doesn't change the value,so remove it from the expression

- 1604040 a^{4} = - 45

Change the signs on both sides of the equation

1604040 a^{4} = 45

Divide both sides

\frac{1604040 a ^{4}}{1604040} = \frac{45}{1604040}

Divide the numbers

a^{4} = \frac{45}{1604040}

Cancel out the common factor 15

a^{4} = \frac{3}{106936}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 4 \frac{3}{106936}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{106936}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 3}{4 106936}

Multiply by the Conjugate

\frac{4 3 \times 4 10693 6 ^{3}}{4 106936 \times 4 10693 6 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 3 \times 10693 6 ^{3}}{4 106936 \times 4 10693 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

4106936 \times 4 10693 6^{3}

The product of roots with the same index is equal to the root of the product

4 106936 \times 10693 6^{3}

Calculate the product

4 10693 6^{4}

Reduce the index of the radical and exponent with 4

106936

\frac{4 3 \times 10693 6 ^{3}}{106936}

a = \pm \frac{4 3 \times 10693 6 ^{3}}{106936}

Separate the equation into 2 possible cases

a = \frac{4 3 \times 10693 6 ^{3}}{106936} a = - \frac{4 3 \times 10693 6 ^{3}}{106936}

Solution

a_{1} = - \frac{4 3 \times 10693 6 ^{3}}{106936}, a_{2} = \frac{4 3 \times 10693 6 ^{3}}{106936}

Alternative Form

a_{1} \approx - 0.072778, a_{2} \approx 0.072778

Show Solution