Using quadratics, find the value of x.

x = 4

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(3x + 1)² = (x + 1)² + (2x + 4)² ← expand all factors using FOIL

9x² + 6x + 1 = x² + 2x + 1 + 4x² + 16x + 16 , simplify right side

9x² + 6x + 1 = 5x² + 18x + 17 ( subtract 5x² + 18x + 17 from both sides )

4x² - 12x - 16 = 0 ( divide through by 4 )

x² - 3x - 4 = 0 ← in standard form

(x - 4)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 1 = 0 ⇒ x = - 1

However, x > 0 thus x = 4