Solve 4x^22x^2x^22x= 6x^24x

Question

Solve the equation

x_{1} = - \frac{4 24}{2}, x_{2} = 0, x_{3} = \frac{4 24}{2}

Alternative Form

x_{1} \approx - 1.106682, x_{2} = 0, x_{3} \approx 1.106682

Evaluate

4 x^{2} \times 2 x^{2} \times x^{2} \times 2 x = 6 x^{2} \times 4 x

Simplify

x^{2} \times 2 x^{2} \times x^{2} \times 2 x = 6 x^{2} \times x

Multiply

More Steps

Evaluate

x^{2} \times 2 x^{2} \times x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{7} \times 2 \times 2

Multiply the terms

x^{7} \times 4

Use the commutative property to reorder the terms

4 x^{7}

4 x^{7} = 6 x^{2} \times x

Multiply

More Steps

Evaluate

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

4 x^{7} = 6 x^{3}

Add or subtract both sides

4 x^{7} - 6 x^{3} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

2 x^{4} - 3 = 0

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

2 x^{4} = 0 + 3

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

2 x^{4} = 3

Divide both sides

\frac{2 x ^{4}}{2} = \frac{3}{2}

Divide the numbers

x^{4} = \frac{3}{2}

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

x = \pm 4 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{2}

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

\frac{4 3}{4 2}

Multiply by the Conjugate

\frac{4 3 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 3 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 24}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 24}{2}

x = \pm \frac{4 24}{2}

Separate the equation into 2 possible cases

x = \frac{4 24}{2} x = - \frac{4 24}{2}

x = 0 x = \frac{4 24}{2} x = - \frac{4 24}{2}

Solution

x_{1} = - \frac{4 24}{2}, x_{2} = 0, x_{3} = \frac{4 24}{2}

Alternative Form

x_{1} \approx - 1.106682, x_{2} = 0, x_{3} \approx 1.106682

Show Solution