Solve 20/58-3x^4 - Socratic AI (ScanMath)

Question

Simplify the expression

\frac{10}{29} - 3 x^{4}

Evaluate

\frac{20}{58} - 3 x^{4}

Solution

\frac{10}{29} - 3 x^{4}

Show Solution

\frac{1}{29} (10 - 87 x^{4})

Evaluate

\frac{20}{58} - 3 x^{4}

Cancel out the common factor 2

\frac{10}{29} - 3 x^{4}

Solution

\frac{1}{29} (10 - 87 x^{4})

Show Solution

x_{1} = - \frac{4 10 \times 8 7 ^{3}}{87}, x_{2} = \frac{4 10 \times 8 7 ^{3}}{87}

Alternative Form

x_{1} \approx - 0.582264, x_{2} \approx 0.582264

Evaluate

\frac{20}{58} - 3 x^{4}

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

\frac{20}{58} - 3 x^{4} = 0

Cancel out the common factor 2

\frac{10}{29} - 3 x^{4} = 0

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

- 3 x^{4} = 0 - \frac{10}{29}

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

- 3 x^{4} = - \frac{10}{29}

Change the signs on both sides of the equation

3 x^{4} = \frac{10}{29}

Multiply by the reciprocal

3 x^{4} \times \frac{1}{3} = \frac{10}{29} \times \frac{1}{3}

Multiply

x^{4} = \frac{10}{29} \times \frac{1}{3}

Multiply

More Steps

Evaluate

\frac{10}{29} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{10}{29 \times 3}

Multiply the numbers

\frac{10}{87}

x^{4} = \frac{10}{87}

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

x = \pm 4 \frac{10}{87}

Simplify the expression

More Steps

Evaluate

4 \frac{10}{87}

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

\frac{4 10}{4 87}

Multiply by the Conjugate

\frac{4 10 \times 4 8 7 ^{3}}{4 87 \times 4 8 7 ^{3}}

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

\frac{4 10 \times 8 7 ^{3}}{4 87 \times 4 8 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

487 \times 4 8 7^{3}

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

4 87 \times 8 7^{3}

Calculate the product

4 8 7^{4}

Reduce the index of the radical and exponent with 4

87

\frac{4 10 \times 8 7 ^{3}}{87}

x = \pm \frac{4 10 \times 8 7 ^{3}}{87}

Separate the equation into 2 possible cases

x = \frac{4 10 \times 8 7 ^{3}}{87} x = - \frac{4 10 \times 8 7 ^{3}}{87}

Solution

x_{1} = - \frac{4 10 \times 8 7 ^{3}}{87}, x_{2} = \frac{4 10 \times 8 7 ^{3}}{87}

Alternative Form

x_{1} \approx - 0.582264, x_{2} \approx 0.582264

Show Solution