Pythagoras theorem states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can represent the length of the hypotenuse as "c", and the lengths of the other two sides as "a" and "b". So the equation is:
c² = a² + b²
To form an equation in x we can use a and b as variable, so we can substitute a = x and b = x-3, the equation becomes:
c² = x² + (x-3)²
To solve for c we can expand the second square and get:
c² = x² + x² - 6x + 9
Now we can add x² on both sides and get:
x² + x² = 6x - 9 + c²
We can combine like terms and get:
2x² = 6x - 9 + c²
Now we can move all the terms to one side and get:
2x² - 6x + 9 - c² = 0
Now we have an equation of a quadratic form with variable x, which can be solved using the quadratic formula.
x² = (6/2)x - 9/2 = 3x - 9/2 = 3x - 4.5 = 0
It can also be factored to get the solutions x = 4.5, x = 0
So the solutions to this equation are x = 4.5, x = 0.