Question

Please find the value of x.

Answer 1

The circle is made up of 2 lines, this means that they will equal each other.

x(x + 1) = 10 * 9

~Simplify

x² + x = 90

~Subtract 90 to both sides

x² + x - 90 = 90 - 90

~Simplify

x² + x - 90 = 0

~Factor out

(x - 9)(x + 10) = 0

~Set both factors to equal 0

x - 9 = 0

x + 10 = 0

~Solve for x in [ x - 9 = 0 ]

x - 9 + 9 = 0 + 9

x = 9

~Solve for x in [ x + 10 = 0 ]

x + 10 - 10 = 10 - 10

x = -10

Since -10 is negative, we can't use it.

Therefore, x = 9

Best of Luck!

Answer 2

x=9

Explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

x* (x+1) = 10*9

Distribute

x^2 +x = 90

Subtract 90 from each side

x^2 +x-90 =0

Factor

(x-9)(x+10) =0

Using the zero product property

x-9=0 x+10=0

x=9 x=-10

Since we cannot have a negative length

x=9