Which of the following is the value of x to the nearest tenth? -2.8 -4.2 -4.8 -6.9

The correct answer is 4.8.

This forms a right triangle, so we will use the Pythagorean theorem.  The radius x forms one leg of the triangle; 14 is the other leg; and (x+10) forms the hypotenuse:

x²+14²=(x+10)²
x²+196=(x+10)(x+10)
x²+196=x*x+10*x+10*x+10*10
x²+196=x²+10x+10x+100
x²+196=x²+20x+100

Subtract x² from both sides:
x²+196-x²=x²+20x+100-x²
196=20x+100

Subtract 100 from both sides:
196-100 = 20x+100-100
96=20x

Divide both sides by 20:
96/20 = 20x/20
4.8 = x