Solve 12x -15x^214x -5x^2

Question

Simplify the expression

12 x - 210 x^{3} - 5 x^{2}

Evaluate

12 x - 15 x^{2} \times 14 x - 5 x^{2}

Solution

More Steps

Evaluate

- 15 x^{2} \times 14 x

Multiply the terms

- 210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 210 x^{2 + 1}

Add the numbers

- 210 x^{3}

12 x - 210 x^{3} - 5 x^{2}

Show Solution

Factor the expression

x (12 - 210 x^{2} - 5 x)

Evaluate

12 x - 15 x^{2} \times 14 x - 5 x^{2}

Multiply

More Steps

Evaluate

15 x^{2} \times 14 x

Multiply the terms

210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

210 x^{2 + 1}

Add the numbers

210 x^{3}

12 x - 210 x^{3} - 5 x^{2}

Rewrite the expression

x \times 12 - x \times 210 x^{2} - x \times 5 x

Solution

x (12 - 210 x^{2} - 5 x)

Show Solution

Find the roots

x_{1} = - \frac{5 + 10105}{420}, x_{2} = 0, x_{3} = \frac{- 5 + 10105}{420}

Alternative Form

x_{1} \approx - 0.251247, x_{2} = 0, x_{3} \approx 0.227437

Evaluate

12 x - 15 x^{2} \times 14 x - 5 x^{2}

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

12 x - 15 x^{2} \times 14 x - 5 x^{2} = 0

Multiply

More Steps

Multiply the terms

15 x^{2} \times 14 x

Multiply the terms

210 x^{2} \times x

Multiply the terms with the same base by adding their exponents

210 x^{2 + 1}

Add the numbers

210 x^{3}

12 x - 210 x^{3} - 5 x^{2} = 0

Factor the expression

x (12 - 210 x^{2} - 5 x) = 0

Separate the equation into 2 possible cases

x = 0 12 - 210 x^{2} - 5 x = 0

Solve the equation

More Steps

Evaluate

12 - 210 x^{2} - 5 x = 0

Rewrite in standard form

- 210 x^{2} - 5 x + 12 = 0

Multiply both sides

210 x^{2} + 5 x - 12 = 0

Substitute a= 210,b= 5 and c= - 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 \times 210 ( - 12 )}{2 \times 210}

Simplify the expression

x = \frac{- 5 \pm 5 ^{2} - 4 \times 210 ( - 12 )}{420}

Simplify the expression

More Steps

Evaluate

5^{2} - 4 \times 210 (- 12)

Multiply

5^{2} - (- 10080)

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

5^{2} + 10080

Evaluate the power

25 + 10080

Add the numbers

10105

x = \frac{- 5 \pm 10105}{420}

Separate the equation into 2 possible cases

x = \frac{- 5 + 10105}{420} x = \frac{- 5 - 10105}{420}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = \frac{- 5 + 10105}{420} x = - \frac{5 + 10105}{420}

x = 0 x = \frac{- 5 + 10105}{420} x = - \frac{5 + 10105}{420}

Solution

x_{1} = - \frac{5 + 10105}{420}, x_{2} = 0, x_{3} = \frac{- 5 + 10105}{420}

Alternative Form

x_{1} \approx - 0.251247, x_{2} = 0, x_{3} \approx 0.227437

Show Solution