x=5
4
4×(4+5)=(x−2)⋅(x−2+x+4)
Simplify the equation: 36 = (x-2)(2x+2)
4 Factor out the common factor of 2 from the right side of the equation: 18 = (x-2)(x+1)
5 Set the equation equal to zero to find the values of x:
x
2
−
x
−
20
=
0
x
2
−x−20=0
6 Factor the quadratic equation: (x+4)(x-5) = 0
7 Solve for x by setting each factor equal to zero and considering only the positive solution since x represents a length: x = 5.
Therefore, the value of x is 5.
