Segments Formed by Two Secants

x, 3, 4, and 6
are the segments
formed by two intersecting secants.

So x(x + 3) = 4(4 + 6).

x(x + 3) = x² + 3x

Multiply a Monomial and a Polynomial

4 + 6 = 10

4⋅10 = 40

Move 40 to the left side.

Factor the right side
x² + 3x - 40.

Find a pair of numbers
whose product is the constant term -40
and whose sum is the coefficient of the middle term +3.

-5⋅8 = -40
-5 + 8 = +3

Then (x - 5)(x + 8) = 0.

Factor a Quadratic Trinomial

Solve the quadratic equation.

Case 1) x - 5 = 0
Then x = 5.
This is the answer for case 1.

Case 2) x + 8 = 0
Then x = -8.

x is a segment.
So x cannot be minus.
So x = -8 cannot be the answer.

Case 1) x = 5
Case 2) No root

So x = 5.

So x = 5 is the answer.