Solve for x:
x^2 = (x - 20)^2 + (x - 10)^2
Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
x^2 = 2 x^2 - 60 x + 500
Move everything to the left hand side.
Subtract 2 x^2 - 60 x + 500 from both sides:
-x^2 + 60 x - 500 = 0
Factor the left hand side.
The left hand side factors into a product with three terms:
-(x - 50) (x - 10) = 0
Multiply both sides by a constant to simplify the equation.
Multiply both sides by -1:
(x - 50) (x - 10) = 0
Find the roots of each term in the product separately.
Split into two equations:
x - 50 = 0 or x - 10 = 0
Look at the first equation: Solve for x.
Add 50 to both sides:
x = 50 or x - 10 = 0
Look at the second equation: Solve for x.
Add 10 to both sides:
x = 50 or x = 10{Discard}
x = 50 feet - length of the ladder.
50 - 10 = 40 feet - The height of the side of the building to the top of the ladder.
50 - 20 =30 feet - The distance from the foot of the ladder to the wall.