Solve 12x^2 - 56x^65 = 0

Question

Solve the equation

x_{1} = - \frac{4 3 \times 7 0 ^{3}}{70}, x_{2} = 0, x_{3} = \frac{4 3 \times 7 0 ^{3}}{70}

Alternative Form

x_{1} \approx - 0.454994, x_{2} = 0, x_{3} \approx 0.454994

Evaluate

12 x^{2} - 56 x^{6} \times 5 = 0

Multiply the terms

12 x^{2} - 280 x^{6} = 0

Factor the expression

4 x^{2} (3 - 70 x^{4}) = 0

Divide both sides

x^{2} (3 - 70 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 - 70 x^{4} = 0

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

x = 0 3 - 70 x^{4} = 0

Solve the equation

More Steps

Evaluate

3 - 70 x^{4} = 0

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

- 70 x^{4} = 0 - 3

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

- 70 x^{4} = - 3

Change the signs on both sides of the equation

70 x^{4} = 3

Divide both sides

\frac{70 x ^{4}}{70} = \frac{3}{70}

Divide the numbers

x^{4} = \frac{3}{70}

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

x = \pm 4 \frac{3}{70}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{70}

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

\frac{4 3}{4 70}

Multiply by the Conjugate

\frac{4 3 \times 4 7 0 ^{3}}{4 70 \times 4 7 0 ^{3}}

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

\frac{4 3 \times 7 0 ^{3}}{4 70 \times 4 7 0 ^{3}}

Multiply the numbers

\frac{4 3 \times 7 0 ^{3}}{70}

x = \pm \frac{4 3 \times 7 0 ^{3}}{70}

Separate the equation into 2 possible cases

x = \frac{4 3 \times 7 0 ^{3}}{70} x = - \frac{4 3 \times 7 0 ^{3}}{70}

x = 0 x = \frac{4 3 \times 7 0 ^{3}}{70} x = - \frac{4 3 \times 7 0 ^{3}}{70}

Solution

x_{1} = - \frac{4 3 \times 7 0 ^{3}}{70}, x_{2} = 0, x_{3} = \frac{4 3 \times 7 0 ^{3}}{70}

Alternative Form

x_{1} \approx - 0.454994, x_{2} = 0, x_{3} \approx 0.454994

Show Solution