Solve -2x^2 11x^6 = -x^2 4x 12

Question

Solve the equation

x_{1} = 0, x_{2} = \frac{5 351384}{11}

Alternative Form

x_{1} = 0, x_{2} \approx 1.168863

Evaluate

- 2 x^{2} \times 11 x^{6} = - x^{2} \times 4 x \times 12

Multiply

More Steps

Evaluate

- 2 x^{2} \times 11 x^{6}

Multiply the terms

- 22 x^{2} \times x^{6}

Multiply the terms with the same base by adding their exponents

- 22 x^{2 + 6}

Add the numbers

- 22 x^{8}

- 22 x^{8} = - x^{2} \times 4 x \times 12

Multiply

More Steps

Evaluate

x^{2} \times 4 x \times 12

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4 \times 12

Add the numbers

x^{3} \times 4 \times 12

Multiply the terms

x^{3} \times 48

Use the commutative property to reorder the terms

48 x^{3}

- 22 x^{8} = - 48 x^{3}

Add or subtract both sides

- 22 x^{8} - (- 48 x^{3}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 22 x^{8} + 48 x^{3} = 0

Factor the expression

2 x^{3} (- 11 x^{5} + 24) = 0

Divide both sides

x^{3} (- 11 x^{5} + 24) = 0

Separate the equation into 2 possible cases

x^{3} = 0 - 11 x^{5} + 24 = 0

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

x = 0 - 11 x^{5} + 24 = 0

Solve the equation

More Steps

Evaluate

- 11 x^{5} + 24 = 0

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

- 11 x^{5} = 0 - 24

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

- 11 x^{5} = - 24

Change the signs on both sides of the equation

11 x^{5} = 24

Divide both sides

\frac{11 x ^{5}}{11} = \frac{24}{11}

Divide the numbers

x^{5} = \frac{24}{11}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{24}{11}

Calculate

x = 5 \frac{24}{11}

Simplify the root

More Steps

Evaluate

5 \frac{24}{11}

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

\frac{5 24}{5 11}

Multiply by the Conjugate

\frac{5 24 \times 5 1 1 ^{4}}{5 11 \times 5 1 1 ^{4}}

Simplify

\frac{5 24 \times 5 14641}{5 11 \times 5 1 1 ^{4}}

Multiply the numbers

\frac{5 351384}{5 11 \times 5 1 1 ^{4}}

Multiply the numbers

\frac{5 351384}{11}

x = \frac{5 351384}{11}

x = 0 x = \frac{5 351384}{11}

Solution

x_{1} = 0, x_{2} = \frac{5 351384}{11}

Alternative Form

x_{1} = 0, x_{2} \approx 1.168863

Show Solution

Solve the equation

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