Solve 46x -18x^22x

Question

Simplify the expression

46 x - 36 x^{3}

Evaluate

46 x - 18 x^{2} \times 2 x

Solution

More Steps

Evaluate

18 x^{2} \times 2 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

46 x - 36 x^{3}

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Factor the expression

2 x (23 - 18 x^{2})

Evaluate

46 x - 18 x^{2} \times 2 x

Multiply

More Steps

Evaluate

18 x^{2} \times 2 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

46 x - 36 x^{3}

Rewrite the expression

2 x \times 23 - 2 x \times 18 x^{2}

Solution

2 x (23 - 18 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{46}{6}, x_{2} = 0, x_{3} = \frac{46}{6}

Alternative Form

x_{1} \approx - 1.130388, x_{2} = 0, x_{3} \approx 1.130388

Evaluate

46 x - 18 x^{2} \times 2 x

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

46 x - 18 x^{2} \times 2 x = 0

Multiply

More Steps

Multiply the terms

18 x^{2} \times 2 x

Multiply the terms

36 x^{2} \times x

Multiply the terms with the same base by adding their exponents

36 x^{2 + 1}

Add the numbers

36 x^{3}

46 x - 36 x^{3} = 0

Factor the expression

2 x (23 - 18 x^{2}) = 0

Divide both sides

x (23 - 18 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 23 - 18 x^{2} = 0

Solve the equation

More Steps

Evaluate

23 - 18 x^{2} = 0

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

- 18 x^{2} = 0 - 23

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

- 18 x^{2} = - 23

Change the signs on both sides of the equation

18 x^{2} = 23

Divide both sides

\frac{18 x ^{2}}{18} = \frac{23}{18}

Divide the numbers

x^{2} = \frac{23}{18}

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

x = \pm \frac{23}{18}

Simplify the expression

More Steps

Evaluate

\frac{23}{18}

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

\frac{23}{18}

Simplify the radical expression

\frac{23}{3 2}

Multiply by the Conjugate

\frac{23 \times 2}{3 2 \times 2}

Multiply the numbers

\frac{46}{3 2 \times 2}

Multiply the numbers

\frac{46}{6}

x = \pm \frac{46}{6}

Separate the equation into 2 possible cases

x = \frac{46}{6} x = - \frac{46}{6}

x = 0 x = \frac{46}{6} x = - \frac{46}{6}

Solution

x_{1} = - \frac{46}{6}, x_{2} = 0, x_{3} = \frac{46}{6}

Alternative Form

x_{1} \approx - 1.130388, x_{2} = 0, x_{3} \approx 1.130388

Show Solution