Solve x^4 10x^2-x^27

Question

Simplify the expression

10 x^{6} - 7 x^{2}

Evaluate

x^{4} \times 10 x^{2} - x^{2} \times 7

Multiply

More Steps

Multiply the terms

x^{4} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 10

Add the numbers

x^{6} \times 10

Use the commutative property to reorder the terms

10 x^{6}

10 x^{6} - x^{2} \times 7

Solution

10 x^{6} - 7 x^{2}

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Factor the expression

x^{2} (10 x^{4} - 7)

Evaluate

x^{4} \times 10 x^{2} - x^{2} \times 7

Multiply

More Steps

Multiply the terms

x^{4} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 10

Add the numbers

x^{6} \times 10

Use the commutative property to reorder the terms

10 x^{6}

10 x^{6} - x^{2} \times 7

Use the commutative property to reorder the terms

10 x^{6} - 7 x^{2}

Rewrite the expression

x^{2} \times 10 x^{4} - x^{2} \times 7

Solution

x^{2} (10 x^{4} - 7)

Show Solution

Find the roots

x_{1} = - \frac{4 7000}{10}, x_{2} = 0, x_{3} = \frac{4 7000}{10}

Alternative Form

x_{1} \approx - 0.914691, x_{2} = 0, x_{3} \approx 0.914691

Evaluate

x^{4} \times 10 x^{2} - x^{2} \times 7

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

x^{4} \times 10 x^{2} - x^{2} \times 7 = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 10

Add the numbers

x^{6} \times 10

Use the commutative property to reorder the terms

10 x^{6}

10 x^{6} - x^{2} \times 7 = 0

Use the commutative property to reorder the terms

10 x^{6} - 7 x^{2} = 0

Factor the expression

x^{2} (10 x^{4} - 7) = 0

Separate the equation into 2 possible cases

x^{2} = 0 10 x^{4} - 7 = 0

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

x = 0 10 x^{4} - 7 = 0

Solve the equation

More Steps

Evaluate

10 x^{4} - 7 = 0

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

10 x^{4} = 0 + 7

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

10 x^{4} = 7

Divide both sides

\frac{10 x ^{4}}{10} = \frac{7}{10}

Divide the numbers

x^{4} = \frac{7}{10}

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

x = \pm 4 \frac{7}{10}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{10}

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

\frac{4 7}{4 10}

Multiply by the Conjugate

\frac{4 7 \times 4 1 0 ^{3}}{4 10 \times 4 1 0 ^{3}}

Simplify

\frac{4 7 \times 4 1000}{4 10 \times 4 1 0 ^{3}}

Multiply the numbers

\frac{4 7000}{4 10 \times 4 1 0 ^{3}}

Multiply the numbers

\frac{4 7000}{10}

x = \pm \frac{4 7000}{10}

Separate the equation into 2 possible cases

x = \frac{4 7000}{10} x = - \frac{4 7000}{10}

x = 0 x = \frac{4 7000}{10} x = - \frac{4 7000}{10}

Solution

x_{1} = - \frac{4 7000}{10}, x_{2} = 0, x_{3} = \frac{4 7000}{10}

Alternative Form

x_{1} \approx - 0.914691, x_{2} = 0, x_{3} \approx 0.914691

Show Solution