The  length of a rectangle is 2 less than twice its width. The area is 144 squared centimeters. Which quadratic equation in standard form correctly models the situation, where w represents the width of the rectangle

The quadratic equation which correctly models the situation is,

Let us consider that width is w.

Given that The length of a rectangle is 2 less than twice its width.

 Area of rectangle (A)

The area is 144 squared centimeters.

Hence, the quadratic equation which correctly models the situation is,

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w² - w - 72 = 0

Step-by-step explanation:

l = 2w - 2

A = 144

A = l * w

A = (2w - 2)w

144 = 2w² - 2w

0 = 2w² - 2w - 144

2w² - 2w - 144 = 0 (divide all by 2)

w² - w - 72 = 0

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .