Solve (x^2 -2x) 2 -11(x^2 -2x) 24

Question

Simplify the expression

- 262 x^{2} + 524 x

Evaluate

(x^{2} - 2 x) \times 2 - 11 (x^{2} - 2 x) \times 24

Multiply the terms

2 (x^{2} - 2 x) - 11 (x^{2} - 2 x) \times 24

Multiply the terms

2 (x^{2} - 2 x) - 264 (x^{2} - 2 x)

Expand the expression

More Steps

Calculate

2 (x^{2} - 2 x)

Apply the distributive property

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

Multiply the numbers

2 x^{2} - 4 x

2 x^{2} - 4 x - 264 (x^{2} - 2 x)

Expand the expression

More Steps

Calculate

- 264 (x^{2} - 2 x)

Apply the distributive property

- 264 x^{2} - (- 264 \times 2 x)

Multiply the numbers

- 264 x^{2} - (- 528 x)

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

- 264 x^{2} + 528 x

2 x^{2} - 4 x - 264 x^{2} + 528 x

Subtract the terms

More Steps

Evaluate

2 x^{2} - 264 x^{2}

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

(2 - 264) x^{2}

Subtract the numbers

- 262 x^{2}

- 262 x^{2} - 4 x + 528 x

Solution

More Steps

Evaluate

- 4 x + 528 x

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

(- 4 + 528) x

Add the numbers

524 x

- 262 x^{2} + 524 x

Show Solution

Factor the expression

- 262 x (x - 2)

Evaluate

(x^{2} - 2 x) \times 2 - 11 (x^{2} - 2 x) \times 24

Multiply the terms

2 (x^{2} - 2 x) - 11 (x^{2} - 2 x) \times 24

Multiply the terms

2 (x^{2} - 2 x) - 264 (x^{2} - 2 x)

Subtract the terms

- 131 (2 x^{2} - 4 x)

Factor the expression

More Steps

Evaluate

2 x^{2} - 4 x

Rewrite the expression

2 x \times x - 2 x \times 2

Factor out 2 x from the expression

2 x (x - 2)

- 131 \times 2 x (x - 2)

Solution

- 262 x (x - 2)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2

Evaluate

(x^{2} - 2 x) \times 2 - 11 (x^{2} - 2 x) \times 24

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

(x^{2} - 2 x) \times 2 - 11 (x^{2} - 2 x) \times 24 = 0

Multiply the terms

2 (x^{2} - 2 x) - 11 (x^{2} - 2 x) \times 24 = 0

Multiply the terms

2 (x^{2} - 2 x) - 264 (x^{2} - 2 x) = 0

Subtract the terms

- 131 (2 x^{2} - 4 x) = 0

Change the sign

131 (2 x^{2} - 4 x) = 0

Rewrite the expression

2 x^{2} - 4 x = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 4 x

Rewrite the expression

2 x \times x - 2 x \times 2

Factor out 2 x from the expression

2 x (x - 2)

2 x (x - 2) = 0

When the product of factors equals 0,at least one factor is 0

2 x = 0 x - 2 = 0

Solve the equation for x

x = 0 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 2

Solution

x_{1} = 0, x_{2} = 2

Show Solution