Solve x^3 - 41x + 30

Question

Factor the expression

(x - 6) (x^{2} + 6 x - 5)

Evaluate

x^{3} - 41 x + 30

Calculate

x^{3} + 6 x^{2} - 5 x - 6 x^{2} - 36 x + 30

Rewrite the expression

x \times x^{2} + x \times 6 x - x \times 5 - 6 x^{2} - 6 \times 6 x + 6 \times 5

Factor out x from the expression

x (x^{2} + 6 x - 5) - 6 x^{2} - 6 \times 6 x + 6 \times 5

Factor out - 6 from the expression

x (x^{2} + 6 x - 5) - 6 (x^{2} + 6 x - 5)

Solution

(x - 6) (x^{2} + 6 x - 5)

Show Solution

Find the roots

x_{1} = - 3 - 14, x_{2} = - 3 + 14, x_{3} = 6

Alternative Form

x_{1} \approx - 6.741657, x_{2} \approx 0.741657, x_{3} = 6

Evaluate

x^{3} - 41 x + 30

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

x^{3} - 41 x + 30 = 0

Factor the expression

(x - 6) (x^{2} + 6 x - 5) = 0

Separate the equation into 2 possible cases

x - 6 = 0 x^{2} + 6 x - 5 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 x^{2} + 6 x - 5 = 0

Solve the equation

More Steps

Evaluate

x^{2} + 6 x - 5 = 0

Substitute a= 1,b= 6 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 6 \pm 6 ^{2} - 4 ( - 5 )}{2}

Simplify the expression

More Steps

Evaluate

6^{2} - 4 (- 5)

Multiply the numbers

6^{2} - (- 20)

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

6^{2} + 20

Evaluate the power

36 + 20

Add the numbers

56

x = \frac{- 6 \pm 56}{2}

Simplify the radical expression

More Steps

Evaluate

56

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 14

Write the number in exponential form with the base of 2

2^{2} \times 14

The root of a product is equal to the product of the roots of each factor

2^{2} \times 14

Reduce the index of the radical and exponent with 2

214

x = \frac{- 6 \pm 2 14}{2}

Separate the equation into 2 possible cases

x = \frac{- 6 + 2 14}{2} x = \frac{- 6 - 2 14}{2}

Simplify the expression

x = - 3 + 14 x = \frac{- 6 - 2 14}{2}

Simplify the expression

x = - 3 + 14 x = - 3 - 14

x = 6 x = - 3 + 14 x = - 3 - 14

Solution

x_{1} = - 3 - 14, x_{2} = - 3 + 14, x_{3} = 6

Alternative Form

x_{1} \approx - 6.741657, x_{2} \approx 0.741657, x_{3} = 6

Show Solution