Solve (2x-7)(x-8)

Question

Simplify the expression

2 x^{2} - 23 x + 56

Evaluate

(2 x - 7) (x - 8)

Apply the distributive property

2 x \times x - 2 x \times 8 - 7 x - (- 7 \times 8)

Multiply the terms

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

Multiply the numbers

2 x^{2} - 16 x - 7 x - (- 7 \times 8)

Multiply the numbers

2 x^{2} - 16 x - 7 x - (- 56)

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} - 16 x - 7 x + 56

Solution

More Steps

Evaluate

- 16 x - 7 x

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

(- 16 - 7) x

Subtract the numbers

- 23 x

2 x^{2} - 23 x + 56

Show Solution

Find the roots

x_{1} = \frac{7}{2}, x_{2} = 8

Alternative Form

x_{1} = 3.5, x_{2} = 8

Evaluate

(2 x - 7) (x - 8)

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

(2 x - 7) (x - 8) = 0

Separate the equation into 2 possible cases

2 x - 7 = 0 x - 8 = 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 = \frac{7}{2} x - 8 = 0

Solve the equation

More Steps

Evaluate

x - 8 = 0

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

x = 0 + 8

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

x = 8

x = \frac{7}{2} x = 8

Solution

x_{1} = \frac{7}{2}, x_{2} = 8

Alternative Form

x_{1} = 3.5, x_{2} = 8

Show Solution