Solve [(1500 - x): 50*520]*( x -18)

Question

Simplify the expression

\frac{78936 x - 1404000 - 52 x ^{2}}{5}

Evaluate

((1500 - x) \div 50 \times 520) (x - 18)

Remove the parentheses

(1500 - x) \div 50 \times 520 (x - 18)

Rewrite the expression

\frac{1500 - x}{50} \times 520 (x - 18)

Multiply the terms

More Steps

Multiply the terms

\frac{1500 - x}{50} \times 520

Cancel out the common factor 10

\frac{1500 - x}{5} \times 52

Multiply the terms

\frac{( 1500 - x ) \times 52}{5}

Multiply the terms

\frac{52 ( 1500 - x )}{5}

\frac{52 ( 1500 - x )}{5} (x - 18)

Multiply the terms

\frac{52 ( 1500 - x ) ( x - 18 )}{5}

Solution

More Steps

Evaluate

52 (1500 - x) (x - 18)

Multiply the terms

More Steps

Evaluate

52 (1500 - x)

Apply the distributive property

52 \times 1500 - 52 x

Multiply the numbers

78000 - 52 x

(78000 - 52 x) (x - 18)

Apply the distributive property

78000 x - 78000 \times 18 - 52 x \times x - (- 52 x \times 18)

Multiply the numbers

78000 x - 1404000 - 52 x \times x - (- 52 x \times 18)

Multiply the terms

78000 x - 1404000 - 52 x^{2} - (- 52 x \times 18)

Multiply the numbers

78000 x - 1404000 - 52 x^{2} - (- 936 x)

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

78000 x - 1404000 - 52 x^{2} + 936 x

Add the terms

More Steps

Evaluate

78000 x + 936 x

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

(78000 + 936) x

Add the numbers

78936 x

78936 x - 1404000 - 52 x^{2}

\frac{78936 x - 1404000 - 52 x ^{2}}{5}

Show Solution

Find the roots

x_{1} = 18, x_{2} = 1500

Evaluate

((1500 - x) \div 50 \times 520) (x - 18)

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

((1500 - x) \div 50 \times 520) (x - 18) = 0

Rewrite the expression

(\frac{1500 - x}{50} \times 520) (x - 18) = 0

Multiply the terms

More Steps

Multiply the terms

\frac{1500 - x}{50} \times 520

Cancel out the common factor 10

\frac{1500 - x}{5} \times 52

Multiply the terms

\frac{( 1500 - x ) \times 52}{5}

Multiply the terms

\frac{52 ( 1500 - x )}{5}

\frac{52 ( 1500 - x )}{5} (x - 18) = 0

Multiply the terms

\frac{52 ( 1500 - x ) ( x - 18 )}{5} = 0

Simplify

52 (1500 - x) (x - 18) = 0

Elimination the left coefficient

(1500 - x) (x - 18) = 0

Separate the equation into 2 possible cases

1500 - x = 0 x - 18 = 0

Solve the equation

More Steps

Evaluate

1500 - x = 0

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

- x = 0 - 1500

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

- x = - 1500

Change the signs on both sides of the equation

x = 1500

x = 1500 x - 18 = 0

Solve the equation

More Steps

Evaluate

x - 18 = 0

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

x = 0 + 18

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

x = 18

x = 1500 x = 18

Solution

x_{1} = 18, x_{2} = 1500

Show Solution