Solve 2 [5(34x^52)-(3x^3)]

Question

Simplify the expression

680 x^{5} - 6 x^{3}

Evaluate

2 (5 (34 x^{5} \times 2) - 3 x^{3})

Remove the parentheses

2 (5 \times 34 x^{5} \times 2 - 3 x^{3})

Multiply the terms

More Steps

Evaluate

5 \times 34 \times 2

Multiply the terms

170 \times 2

Multiply the numbers

340

2 (340 x^{5} - 3 x^{3})

Apply the distributive property

2 \times 340 x^{5} - 2 \times 3 x^{3}

Multiply the numbers

680 x^{5} - 2 \times 3 x^{3}

Solution

680 x^{5} - 6 x^{3}

Show Solution

Factor the expression

2 x^{3} (340 x^{2} - 3)

Evaluate

2 (5 (34 x^{5} \times 2) - 3 x^{3})

Remove the parentheses

2 (5 \times 34 x^{5} \times 2 - 3 x^{3})

Multiply the terms

2 (5 \times 68 x^{5} - 3 x^{3})

Multiply the numbers

More Steps

Evaluate

5 \times 68

Multiply the numbers

340

Evaluate

340 x^{5}

2 (340 x^{5} - 3 x^{3})

Solution

More Steps

Evaluate

340 x^{5} - 3 x^{3}

Rewrite the expression

x^{3} \times 340 x^{2} - x^{3} \times 3

Factor out x^{3} from the expression

x^{3} (340 x^{2} - 3)

2 x^{3} (340 x^{2} - 3)

Show Solution

Find the roots

x_{1} = - \frac{255}{170}, x_{2} = 0, x_{3} = \frac{255}{170}

Alternative Form

x_{1} \approx - 0.093934, x_{2} = 0, x_{3} \approx 0.093934

Evaluate

2 (5 (34 x^{5} \times 2) - (3 x^{3}))

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

2 (5 (34 x^{5} \times 2) - (3 x^{3})) = 0

Multiply the terms

2 (5 \times 68 x^{5} - (3 x^{3})) = 0

Multiply the terms

2 (5 \times 68 x^{5} - 3 x^{3}) = 0

Multiply the numbers

2 (340 x^{5} - 3 x^{3}) = 0

Rewrite the expression

340 x^{5} - 3 x^{3} = 0

Factor the expression

x^{3} (340 x^{2} - 3) = 0

Separate the equation into 2 possible cases

x^{3} = 0 340 x^{2} - 3 = 0

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

x = 0 340 x^{2} - 3 = 0

Solve the equation

More Steps

Evaluate

340 x^{2} - 3 = 0

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

340 x^{2} = 0 + 3

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

340 x^{2} = 3

Divide both sides

\frac{340 x ^{2}}{340} = \frac{3}{340}

Divide the numbers

x^{2} = \frac{3}{340}

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

x = \pm \frac{3}{340}

Simplify the expression

More Steps

Evaluate

\frac{3}{340}

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

\frac{3}{340}

Simplify the radical expression

\frac{3}{2 85}

Multiply by the Conjugate

\frac{3 \times 85}{2 85 \times 85}

Multiply the numbers

\frac{255}{2 85 \times 85}

Multiply the numbers

\frac{255}{170}

x = \pm \frac{255}{170}

Separate the equation into 2 possible cases

x = \frac{255}{170} x = - \frac{255}{170}

x = 0 x = \frac{255}{170} x = - \frac{255}{170}

Solution

x_{1} = - \frac{255}{170}, x_{2} = 0, x_{3} = \frac{255}{170}

Alternative Form

x_{1} \approx - 0.093934, x_{2} = 0, x_{3} \approx 0.093934

Show Solution