Solve (2x-1)(x+2)-(x-2)^2-(x+2)^2

Question

Simplify the expression

3 x - 10

Evaluate

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

Expand the expression

More Steps

Calculate

(2 x - 1) (x + 2)

Apply the distributive property

2 x \times x + 2 x \times 2 - x - 2

Multiply the terms

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

Multiply the numbers

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

Subtract the terms

More Steps

Evaluate

4 x - x

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

(4 - 1) x

Subtract the numbers

3 x

2 x^{2} + 3 x - 2

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

Expand the expression

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

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

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

Expand the expression

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

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

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

Subtract the terms

More Steps

Evaluate

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

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

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

Subtract the numbers

0 \times x^{2}

Any expression multiplied by 0 equals 0

0

0 + 3 x - 2 + 4 x - 4 - 4 x - 4

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

3 x - 2 + 4 x - 4 - 4 x - 4

Calculate the sum or difference

More Steps

Evaluate

3 x + 4 x - 4 x

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

(3 + 4 - 4) x

Calculate the sum or difference

3 x

3 x - 2 - 4 - 4

Solution

3 x - 10

Show Solution

Find the roots

x = \frac{10}{3}

Alternative Form

x = 3. \dot{3}

Evaluate

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

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

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

Subtract the terms

More Steps

Simplify

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

Expand the expression

More Steps

Calculate

(2 x - 1) (x + 2)

Apply the distributive property

2 x \times x + 2 x \times 2 - x - 2

Multiply the terms

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

Multiply the numbers

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

Subtract the terms

2 x^{2} + 3 x - 2

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

Expand the expression

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

Subtract the terms

More Steps

Evaluate

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

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

(2 - 1) x^{2}

Subtract the numbers

x^{2}

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

Add the terms

More Steps

Evaluate

3 x + 4 x

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

(3 + 4) x

Add the numbers

7 x

x^{2} + 7 x - 2 - 4

Subtract the numbers

x^{2} + 7 x - 6

x^{2} + 7 x - 6 - (x + 2)^{2} = 0

Calculate the sum or difference

More Steps

Evaluate

x^{2} + 7 x - 6 - (x + 2)^{2}

Expand the expression

x^{2} + 7 x - 6 - x^{2} - 4 x - 4

The sum of two opposites equals 0

More Steps

Evaluate

x^{2} - x^{2}

Collect like terms

(1 - 1) x^{2}

Add the coefficients

0 \times x^{2}

Calculate

0

0 + 7 x - 6 - 4 x - 4

Remove 0

7 x - 6 - 4 x - 4

Subtract the terms

More Steps

Evaluate

7 x - 4 x

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

(7 - 4) x

Subtract the numbers

3 x

3 x - 6 - 4

Subtract the numbers

3 x - 10

3 x - 10 = 0

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

3 x = 0 + 10

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

3 x = 10

Divide both sides

\frac{3 x}{3} = \frac{10}{3}

Solution

x = \frac{10}{3}

Alternative Form

x = 3. \dot{3}

Show Solution