Solve x^3-5x+6x - ScanMath

Question

Simplify the expression

x^{3} + x

Evaluate

x^{3} - 5 x + 6 x

Solution

More Steps

Evaluate

- 5 x + 6 x

Collect like terms by calculating the sum or difference of their coefficients

(- 5 + 6) x

Add the numbers

x

x^{3} + x

Show Solution

x (x^{2} + 1)

Evaluate

x^{3} - 5 x + 6 x

Add the terms

More Steps

Evaluate

- 5 x + 6 x

Collect like terms by calculating the sum or difference of their coefficients

(- 5 + 6) x

Add the numbers

x

x^{3} + x

Rewrite the expression

x \times x^{2} + x

Solution

x (x^{2} + 1)

Show Solution

x_{1} = - i, x_{2} = i, x_{3} = 0

Evaluate

x^{3} - 5 x + 6 x

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

x^{3} - 5 x + 6 x = 0

Add the terms

More Steps

Evaluate

x^{3} - 5 x + 6 x

Add the terms

More Steps

Evaluate

- 5 x + 6 x

Collect like terms by calculating the sum or difference of their coefficients

(- 5 + 6) x

Add the numbers

x

x^{3} + x

x^{3} + x = 0

Factor the expression

x (x^{2} + 1) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

x^{2} + 1 = 0

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

x^{2} = 0 - 1

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

x^{2} = - 1

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

x = \pm - 1

Simplify the expression

x = \pm i

Separate the equation into 2 possible cases

x = i x = - i

x = 0 x = i x = - i

Solution

x_{1} = - i, x_{2} = i, x_{3} = 0

Show Solution