Solve (x-5)(2x-7)

Question

Simplify the expression

2 x^{2} - 17 x + 35

Evaluate

(x - 5) (2 x - 7)

Apply the distributive property

x \times 2 x - x \times 7 - 5 \times 2 x - (- 5 \times 7)

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 7 - 5 \times 2 x - (- 5 \times 7)

Use the commutative property to reorder the terms

2 x^{2} - 7 x - 5 \times 2 x - (- 5 \times 7)

Multiply the numbers

2 x^{2} - 7 x - 10 x - (- 5 \times 7)

Multiply the numbers

2 x^{2} - 7 x - 10 x - (- 35)

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} - 7 x - 10 x + 35

Solution

More Steps

Evaluate

- 7 x - 10 x

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

(- 7 - 10) x

Subtract the numbers

- 17 x

2 x^{2} - 17 x + 35

Show Solution

Find the roots

x_{1} = \frac{7}{2}, x_{2} = 5

Alternative Form

x_{1} = 3.5, x_{2} = 5

Evaluate

(x - 5) (2 x - 7)

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

(x - 5) (2 x - 7) = 0

Separate the equation into 2 possible cases

x - 5 = 0 2 x - 7 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 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 = 5 x = \frac{7}{2}

Solution

x_{1} = \frac{7}{2}, x_{2} = 5

Alternative Form

x_{1} = 3.5, x_{2} = 5

Show Solution