Solve (436610410 x^4 ) - (350410 x^6 )

Question

Factor the expression

10 x^{4} (43661041 - 35041 x^{2})

Evaluate

436610410 x^{4} - 350410 x^{6}

Rewrite the expression

10 x^{4} \times 43661041 - 10 x^{4} \times 35041 x^{2}

Solution

10 x^{4} (43661041 - 35041 x^{2})

Show Solution

x_{1} = - \frac{1529926537681}{35041}, x_{2} = 0, x_{3} = \frac{1529926537681}{35041}

Alternative Form

x_{1} \approx - 35.298707, x_{2} = 0, x_{3} \approx 35.298707

Evaluate

(436610410 x^{4}) - (350410 x^{6})

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

(436610410 x^{4}) - (350410 x^{6}) = 0

Multiply the terms

436610410 x^{4} - (350410 x^{6}) = 0

Multiply the terms

436610410 x^{4} - 350410 x^{6} = 0

Factor the expression

10 x^{4} (43661041 - 35041 x^{2}) = 0

Divide both sides

x^{4} (43661041 - 35041 x^{2}) = 0

Separate the equation into 2 possible cases

x^{4} = 0 43661041 - 35041 x^{2} = 0

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

x = 0 43661041 - 35041 x^{2} = 0

Solve the equation

More Steps

Evaluate

43661041 - 35041 x^{2} = 0

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

- 35041 x^{2} = 0 - 43661041

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

- 35041 x^{2} = - 43661041

Change the signs on both sides of the equation

35041 x^{2} = 43661041

Divide both sides

\frac{35041 x ^{2}}{35041} = \frac{43661041}{35041}

Divide the numbers

x^{2} = \frac{43661041}{35041}

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

x = \pm \frac{43661041}{35041}

Simplify the expression

More Steps

Evaluate

\frac{43661041}{35041}

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

\frac{43661041}{35041}

Multiply by the Conjugate

\frac{43661041 \times 35041}{35041 \times 35041}

Multiply the numbers

\frac{1529926537681}{35041 \times 35041}

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

\frac{1529926537681}{35041}

x = \pm \frac{1529926537681}{35041}

Separate the equation into 2 possible cases

x = \frac{1529926537681}{35041} x = - \frac{1529926537681}{35041}

x = 0 x = \frac{1529926537681}{35041} x = - \frac{1529926537681}{35041}

Solution

x_{1} = - \frac{1529926537681}{35041}, x_{2} = 0, x_{3} = \frac{1529926537681}{35041}

Alternative Form

x_{1} \approx - 35.298707, x_{2} = 0, x_{3} \approx 35.298707

Show Solution