Solve x 77x^3 - x^214x^492

Question

Simplify the expression

77 x^{4} - 1288 x^{6}

Evaluate

x \times 77 x^{3} - x^{2} \times 14 x^{4} \times 92

Multiply

More Steps

Multiply the terms

x \times 77 x^{3}

Multiply the terms with the same base by adding their exponents

x^{1 + 3} \times 77

Add the numbers

x^{4} \times 77

Use the commutative property to reorder the terms

77 x^{4}

77 x^{4} - x^{2} \times 14 x^{4} \times 92

Solution

More Steps

Multiply the terms

x^{2} \times 14 x^{4} \times 92

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 14 \times 92

Add the numbers

x^{6} \times 14 \times 92

Multiply the terms

x^{6} \times 1288

Use the commutative property to reorder the terms

1288 x^{6}

77 x^{4} - 1288 x^{6}

Show Solution

Factor the expression

7 x^{4} (11 - 184 x^{2})

Evaluate

x \times 77 x^{3} - x^{2} \times 14 x^{4} \times 92

Multiply

More Steps

Multiply the terms

x \times 77 x^{3}

Multiply the terms with the same base by adding their exponents

x^{1 + 3} \times 77

Add the numbers

x^{4} \times 77

Use the commutative property to reorder the terms

77 x^{4}

77 x^{4} - x^{2} \times 14 x^{4} \times 92

Multiply

More Steps

Multiply the terms

x^{2} \times 14 x^{4} \times 92

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 14 \times 92

Add the numbers

x^{6} \times 14 \times 92

Multiply the terms

x^{6} \times 1288

Use the commutative property to reorder the terms

1288 x^{6}

77 x^{4} - 1288 x^{6}

Rewrite the expression

7 x^{4} \times 11 - 7 x^{4} \times 184 x^{2}

Solution

7 x^{4} (11 - 184 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{506}{92}, x_{2} = 0, x_{3} = \frac{506}{92}

Alternative Form

x_{1} \approx - 0.244505, x_{2} = 0, x_{3} \approx 0.244505

Evaluate

x \times 77 x^{3} - x^{2} \times 14 x^{4} \times 92

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

x \times 77 x^{3} - x^{2} \times 14 x^{4} \times 92 = 0

Multiply

More Steps

Multiply the terms

x \times 77 x^{3}

Multiply the terms with the same base by adding their exponents

x^{1 + 3} \times 77

Add the numbers

x^{4} \times 77

Use the commutative property to reorder the terms

77 x^{4}

77 x^{4} - x^{2} \times 14 x^{4} \times 92 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 14 x^{4} \times 92

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 14 \times 92

Add the numbers

x^{6} \times 14 \times 92

Multiply the terms

x^{6} \times 1288

Use the commutative property to reorder the terms

1288 x^{6}

77 x^{4} - 1288 x^{6} = 0

Factor the expression

7 x^{4} (11 - 184 x^{2}) = 0

Divide both sides

x^{4} (11 - 184 x^{2}) = 0

Separate the equation into 2 possible cases

x^{4} = 0 11 - 184 x^{2} = 0

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

x = 0 11 - 184 x^{2} = 0

Solve the equation

More Steps

Evaluate

11 - 184 x^{2} = 0

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

- 184 x^{2} = 0 - 11

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

- 184 x^{2} = - 11

Change the signs on both sides of the equation

184 x^{2} = 11

Divide both sides

\frac{184 x ^{2}}{184} = \frac{11}{184}

Divide the numbers

x^{2} = \frac{11}{184}

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

x = \pm \frac{11}{184}

Simplify the expression

More Steps

Evaluate

\frac{11}{184}

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

\frac{11}{184}

Simplify the radical expression

\frac{11}{2 46}

Multiply by the Conjugate

\frac{11 \times 46}{2 46 \times 46}

Multiply the numbers

\frac{506}{2 46 \times 46}

Multiply the numbers

\frac{506}{92}

x = \pm \frac{506}{92}

Separate the equation into 2 possible cases

x = \frac{506}{92} x = - \frac{506}{92}

x = 0 x = \frac{506}{92} x = - \frac{506}{92}

Solution

x_{1} = - \frac{506}{92}, x_{2} = 0, x_{3} = \frac{506}{92}

Alternative Form

x_{1} \approx - 0.244505, x_{2} = 0, x_{3} \approx 0.244505

Show Solution