Solve 2x^4 x^3-8x^2 6

Question

Simplify the expression

2 x^{7} - 48 x^{2}

Evaluate

2 x^{4} \times x^{3} - 8 x^{2} \times 6

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - 8 x^{2} \times 6

Solution

2 x^{7} - 48 x^{2}

Show Solution

2 x^{2} (x^{5} - 24)

Evaluate

2 x^{4} \times x^{3} - 8 x^{2} \times 6

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - 8 x^{2} \times 6

Multiply the terms

2 x^{7} - 48 x^{2}

Rewrite the expression

2 x^{2} \times x^{5} - 2 x^{2} \times 24

Solution

2 x^{2} (x^{5} - 24)

Show Solution

x_{1} = 0, x_{2} = 524

Alternative Form

x_{1} = 0, x_{2} \approx 1.888175

Evaluate

2 x^{4} \times x^{3} - 8 x^{2} \times 6

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

2 x^{4} \times x^{3} - 8 x^{2} \times 6 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{4 + 3}

Add the numbers

2 x^{7}

2 x^{7} - 8 x^{2} \times 6 = 0

Multiply the terms

2 x^{7} - 48 x^{2} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

x^{2} = 0 x^{5} - 24 = 0

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

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

Solve the equation

More Steps

Evaluate

x^{5} - 24 = 0

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

x^{5} = 0 + 24

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

x^{5} = 24

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

5 x^{5} = 524

Calculate

x = 524

x = 0 x = 524

Solution

x_{1} = 0, x_{2} = 524

Alternative Form

x_{1} = 0, x_{2} \approx 1.888175

Show Solution