Solve x^42x-7 - ScanMath

Question

Simplify the expression

2 x^{5} - 7

Evaluate

x^{4} \times 2 x - 7

Solution

More Steps

Evaluate

x^{4} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{4 + 1} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 7

Show Solution

x = \frac{5 112}{2}

Alternative Form

x \approx 1.284735

Evaluate

x^{4} \times 2 x - 7

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

x^{4} \times 2 x - 7 = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{4 + 1} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} - 7 = 0

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

2 x^{5} = 0 + 7

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

2 x^{5} = 7

Divide both sides

\frac{2 x ^{5}}{2} = \frac{7}{2}

Divide the numbers

x^{5} = \frac{7}{2}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{7}{2}

Calculate

x = 5 \frac{7}{2}

Solution

More Steps

Evaluate

5 \frac{7}{2}

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

\frac{5 7}{5 2}

Multiply by the Conjugate

\frac{5 7 \times 5 2 ^{4}}{5 2 \times 5 2 ^{4}}

Simplify

\frac{5 7 \times 5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

57 \times 516

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

5 7 \times 16

Calculate the product

5112

\frac{5 112}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

52 \times 5 2^{4}

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

5 2 \times 2^{4}

Calculate the product

5 2^{5}

Reduce the index of the radical and exponent with 5

2

\frac{5 112}{2}

x = \frac{5 112}{2}

Alternative Form

x \approx 1.284735

Show Solution