Solve (30-2x)(25-2x)

Question

Simplify the expression

750 - 110 x + 4 x^{2}

Evaluate

(30 - 2 x) (25 - 2 x)

Apply the distributive property

30 \times 25 - 30 \times 2 x - 2 x \times 25 - (- 2 x \times 2 x)

Multiply the numbers

750 - 30 \times 2 x - 2 x \times 25 - (- 2 x \times 2 x)

Multiply the numbers

750 - 60 x - 2 x \times 25 - (- 2 x \times 2 x)

Multiply the numbers

750 - 60 x - 50 x - (- 2 x \times 2 x)

Multiply the terms

More Steps

Evaluate

- 2 x \times 2 x

Multiply the numbers

- 4 x \times x

Multiply the terms

- 4 x^{2}

750 - 60 x - 50 x - (- 4 x^{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

750 - 60 x - 50 x + 4 x^{2}

Solution

More Steps

Evaluate

- 60 x - 50 x

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

(- 60 - 50) x

Subtract the numbers

- 110 x

750 - 110 x + 4 x^{2}

Show Solution

Factor the expression

2 (15 - x) (25 - 2 x)

Evaluate

(30 - 2 x) (25 - 2 x)

Solution

2 (15 - x) (25 - 2 x)

Show Solution

Find the roots

x_{1} = \frac{25}{2}, x_{2} = 15

Alternative Form

x_{1} = 12.5, x_{2} = 15

Evaluate

(30 - 2 x) (25 - 2 x)

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

(30 - 2 x) (25 - 2 x) = 0

Separate the equation into 2 possible cases

30 - 2 x = 0 25 - 2 x = 0

Solve the equation

More Steps

Evaluate

30 - 2 x = 0

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

- 2 x = 0 - 30

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

- 2 x = - 30

Change the signs on both sides of the equation

2 x = 30

Divide both sides

\frac{2 x}{2} = \frac{30}{2}

Divide the numbers

x = \frac{30}{2}

Divide the numbers

More Steps

Evaluate

\frac{30}{2}

Reduce the numbers

\frac{15}{1}

Calculate

15

x = 15

x = 15 25 - 2 x = 0

Solve the equation

More Steps

Evaluate

25 - 2 x = 0

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

- 2 x = 0 - 25

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

- 2 x = - 25

Change the signs on both sides of the equation

2 x = 25

Divide both sides

\frac{2 x}{2} = \frac{25}{2}

Divide the numbers

x = \frac{25}{2}

x = 15 x = \frac{25}{2}

Solution

x_{1} = \frac{25}{2}, x_{2} = 15

Alternative Form

x_{1} = 12.5, x_{2} = 15

Show Solution