Solve (2x - 4)(2x - 7)

Question

Simplify the expression

4 x^{2} - 22 x + 28

Evaluate

(2 x - 4) (2 x - 7)

Apply the distributive property

2 x \times 2 x - 2 x \times 7 - 4 \times 2 x - (- 4 \times 7)

Multiply the terms

More Steps

Evaluate

2 x \times 2 x

Multiply the numbers

4 x \times x

Multiply the terms

4 x^{2}

4 x^{2} - 2 x \times 7 - 4 \times 2 x - (- 4 \times 7)

Multiply the numbers

4 x^{2} - 14 x - 4 \times 2 x - (- 4 \times 7)

Multiply the numbers

4 x^{2} - 14 x - 8 x - (- 4 \times 7)

Multiply the numbers

4 x^{2} - 14 x - 8 x - (- 28)

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

4 x^{2} - 14 x - 8 x + 28

Solution

More Steps

Evaluate

- 14 x - 8 x

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

(- 14 - 8) x

Subtract the numbers

- 22 x

4 x^{2} - 22 x + 28

Show Solution

Factor the expression

2 (x - 2) (2 x - 7)

Evaluate

(2 x - 4) (2 x - 7)

Solution

2 (x - 2) (2 x - 7)

Show Solution

Find the roots

x_{1} = 2, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = 2, x_{2} = 3.5

Evaluate

(2 x - 4) (2 x - 7)

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

(2 x - 4) (2 x - 7) = 0

Separate the equation into 2 possible cases

2 x - 4 = 0 2 x - 7 = 0

Solve the equation

More Steps

Evaluate

2 x - 4 = 0

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

2 x = 0 + 4

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

2 x = 4

Divide both sides

\frac{2 x}{2} = \frac{4}{2}

Divide the numbers

x = \frac{4}{2}

Divide the numbers

More Steps

Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

x = 2

x = 2 2 x - 7 = 0

Solve the equation

More Steps

Evaluate

2 x - 7 = 0

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

2 x = 0 + 7

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

2 x = 7

Divide both sides

\frac{2 x}{2} = \frac{7}{2}

Divide the numbers

x = \frac{7}{2}

x = 2 x = \frac{7}{2}

Solution

x_{1} = 2, x_{2} = \frac{7}{2}

Alternative Form

x_{1} = 2, x_{2} = 3.5

Show Solution