Solve x^34x-5 - ScanMath

Question

Simplify the expression

4 x^{4} - 5

Evaluate

x^{3} \times 4 x - 5

Solution

More Steps

Evaluate

x^{3} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 4

Add the numbers

x^{4} \times 4

Use the commutative property to reorder the terms

4 x^{4}

4 x^{4} - 5

Show Solution

x_{1} = - \frac{4 20}{2}, x_{2} = \frac{4 20}{2}

Alternative Form

x_{1} \approx - 1.057371, x_{2} \approx 1.057371

Evaluate

x^{3} \times 4 x - 5

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

x^{3} \times 4 x - 5 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{3 + 1} \times 4

Add the numbers

x^{4} \times 4

Use the commutative property to reorder the terms

4 x^{4}

4 x^{4} - 5 = 0

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

4 x^{4} = 0 + 5

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

4 x^{4} = 5

Divide both sides

\frac{4 x ^{4}}{4} = \frac{5}{4}

Divide the numbers

x^{4} = \frac{5}{4}

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

x = \pm 4 \frac{5}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{4}

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

\frac{4 5}{4 4}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{4 5}{2}

Multiply by the Conjugate

\frac{4 5 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

45 \times 2

Use n a = mn a^{m} to expand the expression

45 \times 4 2^{2}

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

4 5 \times 2^{2}

Calculate the product

420

\frac{4 20}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 20}{2}

x = \pm \frac{4 20}{2}

Separate the equation into 2 possible cases

x = \frac{4 20}{2} x = - \frac{4 20}{2}

Solution

x_{1} = - \frac{4 20}{2}, x_{2} = \frac{4 20}{2}

Alternative Form

x_{1} \approx - 1.057371, x_{2} \approx 1.057371

Show Solution