Solve (x-2)^2-3x(x-2)

Question

Simplify the expression

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

Evaluate

(x - 2)^{2} - 3 x (x - 2)

Expand the expression

x^{2} - 4 x + 4 - 3 x (x - 2)

Expand the expression

More Steps

Calculate

- 3 x (x - 2)

Apply the distributive property

- 3 x \times x - (- 3 x \times 2)

Multiply the terms

- 3 x^{2} - (- 3 x \times 2)

Multiply the numbers

- 3 x^{2} - (- 6 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

- 3 x^{2} + 6 x

x^{2} - 4 x + 4 - 3 x^{2} + 6 x

Subtract the terms

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Evaluate

x^{2} - 3 x^{2}

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

(1 - 3) x^{2}

Subtract the numbers

- 2 x^{2}

- 2 x^{2} - 4 x + 4 + 6 x

Solution

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Evaluate

- 4 x + 6 x

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

(- 4 + 6) x

Add the numbers

2 x

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

Show Solution

Factor the expression

- 2 (x + 1) (x - 2)

Evaluate

(x - 2)^{2} - 3 x (x - 2)

Rewrite the expression

(x - 2) (x - 2) - 3 x (x - 2)

Factor out x - 2 from the expression

(x - 2 - 3 x) (x - 2)

Solution

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Evaluate

x - 2 - 3 x

Subtract the terms

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Evaluate

x - 3 x

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

(1 - 3) x

Subtract the numbers

- 2 x

- 2 x - 2

Factor the expression

- 2 (x + 1)

- 2 (x + 1) (x - 2)

Show Solution

Find the roots

x_{1} = - 1, x_{2} = 2

Evaluate

(x - 2)^{2} - 3 x (x - 2)

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

(x - 2)^{2} - 3 x (x - 2) = 0

Calculate

More Steps

Evaluate

(x - 2)^{2} - 3 x (x - 2)

Expand the expression

x^{2} - 4 x + 4 - 3 x (x - 2)

Expand the expression

More Steps

Calculate

- 3 x (x - 2)

Apply the distributive property

- 3 x \times x - (- 3 x \times 2)

Multiply the terms

- 3 x^{2} - (- 3 x \times 2)

Multiply the numbers

- 3 x^{2} - (- 6 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

- 3 x^{2} + 6 x

x^{2} - 4 x + 4 - 3 x^{2} + 6 x

Subtract the terms

More Steps

Evaluate

x^{2} - 3 x^{2}

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

(1 - 3) x^{2}

Subtract the numbers

- 2 x^{2}

- 2 x^{2} - 4 x + 4 + 6 x

Add the terms

More Steps

Evaluate

- 4 x + 6 x

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

(- 4 + 6) x

Add the numbers

2 x

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

- 2 x^{2} + 2 x + 4 = 0

Factor the expression

More Steps

Evaluate

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

Rewrite the expression

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

Factor out - 2 from the expression

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

Factor the expression

More Steps

Evaluate

x^{2} - x - 2

Rewrite the expression

x^{2} + (1 - 2) x - 2

Calculate

x^{2} + x - 2 x - 2

Rewrite the expression

x \times x + x - 2 x - 2

Factor out x from the expression

x (x + 1) - 2 x - 2

Factor out - 2 from the expression

x (x + 1) - 2 (x + 1)

Factor out x + 1 from the expression

(x - 2) (x + 1)

- 2 (x - 2) (x + 1)

- 2 (x - 2) (x + 1) = 0

Divide the terms

(x - 2) (x + 1) = 0

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

x - 2 = 0 x + 1 = 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 = 2 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = 2 x = - 1

Solution

x_{1} = - 1, x_{2} = 2

Show Solution