Question

The area of the opening of a rectangular window is to be 143 square feet. If the length is to be 2 feet more than the width, what are the dimensions?

Answer 1

Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
\(x^2+2 x = 143\)
Take one half of the coefficient of x and square it, then add it to both sides.
Add 1 to both sides:
\(x^2+2 x+1 = 144\)
Factor the left hand side.
Write the left hand side as a square:
\((x+1)^2 = 144\)
Eliminate the exponent on the left hand side.
Take the square root of both sides:
\(x+1 = 12\) or \(x+1 = -12\)
Look at the first equation: Solve for x.
Subtract 1 from both sides:
\(x = 11\) or \(x+1 = -12\)
Look at the second equation: Solve for x.
Subtract 1 from both sides...

Answer 2

Which leaves you with?

Answer 3

11 by 13?

Answer 4

@DangerousJesse