Solve (x^32x^2 -29x^43) / (x 7)

Question

Simplify the expression

\frac{2 x ^{4} - 87 x ^{3}}{7}

Evaluate

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7}

Multiply

More Steps

Multiply the terms

x^{3} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

\frac{2 x ^{5} - 29 x ^{4} \times 3}{x \times 7}

Multiply the terms

\frac{2 x ^{5} - 87 x ^{4}}{x \times 7}

Use the commutative property to reorder the terms

\frac{2 x ^{5} - 87 x ^{4}}{7 x}

Factor

\frac{x ( 2 x ^{4} - 87 x ^{3} )}{7 x}

Solution

\frac{2 x ^{4} - 87 x ^{3}}{7}

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Find the excluded values

x = 0

Evaluate

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7}

To find the excluded values,set the denominators equal to 0

x \times 7 = 0

Use the commutative property to reorder the terms

7 x = 0

Solution

x = 0

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Find the roots

x = \frac{87}{2}

Alternative Form

x = 43.5

Evaluate

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7}

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

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7} = 0

Find the domain

More Steps

Evaluate

x \times 7 \neq = 0

Use the commutative property to reorder the terms

7 x \neq = 0

Rewrite the expression

x \neq = 0

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7} = 0, x \neq = 0

Calculate

\frac{x ^{3} \times 2 x ^{2} - 29 x ^{4} \times 3}{x \times 7} = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

\frac{2 x ^{5} - 29 x ^{4} \times 3}{x \times 7} = 0

Multiply the terms

\frac{2 x ^{5} - 87 x ^{4}}{x \times 7} = 0

Use the commutative property to reorder the terms

\frac{2 x ^{5} - 87 x ^{4}}{7 x} = 0

Divide the terms

More Steps

Evaluate

\frac{2 x ^{5} - 87 x ^{4}}{7 x}

Factor

\frac{x ( 2 x ^{4} - 87 x ^{3} )}{7 x}

Reduce the fraction

\frac{2 x ^{4} - 87 x ^{3}}{7}

\frac{2 x ^{4} - 87 x ^{3}}{7} = 0

Simplify

2 x^{4} - 87 x^{3} = 0

Factor the expression

x^{3} (2 x - 87) = 0

Separate the equation into 2 possible cases

x^{3} = 0 2 x - 87 = 0

The only way a power can be 0 is when the base equals 0

x = 0 2 x - 87 = 0

Solve the equation

More Steps

Evaluate

2 x - 87 = 0

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

2 x = 0 + 87

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

2 x = 87

Divide both sides

\frac{2 x}{2} = \frac{87}{2}

Divide the numbers

x = \frac{87}{2}

x = 0 x = \frac{87}{2}

Check if the solution is in the defined range

x = 0 x = \frac{87}{2}, x \neq = 0

Solution

x = \frac{87}{2}

Alternative Form

x = 43.5

Show Solution