Solve for x: (x-7)^2+(x-3)^2 = 225 Expand out terms of the left hand side: 2 x^2-20 x+58 = 225 Divide both sides by 2: x^2-10 x+29 = 225/2 Subtract 29 from both sides: x^2-10 x = 167/2 Add 25 to both sides: x^2-10 x+25 = 217/2 Write the left hand side as a square: (x-5)^2 = 217/2 Take the square root of both sides: x-5 = sqrt(217/2) or x-5 = -sqrt(217/2) Add 5 to both sides: x = 5+sqrt(217/2) or x-5 = -sqrt(217/2) Add 5 to both sides: Answer: | | x = 5+sqrt(217/2) or x = 5-sqrt(217/2)
This circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and r=radius
r^2 = 225 so r = sqrt225 = 15
Solve for x: (x-7)^2+(x-3)^2 = 225 Expand out terms of the left hand side: 2 x^2-20 x+58 = 225 Divide both sides by 2: x^2-10 x+29 = 225/2 Subtract 29 from both sides: x^2-10 x = 167/2 Add 25 to both sides: x^2-10 x+25 = 217/2 Write the left hand side as a square: (x-5)^2 = 217/2 Take the square root of both sides: x-5 = sqrt(217/2) or x-5 = -sqrt(217/2) Add 5 to both sides: x = 5+sqrt(217/2) or x-5 = -sqrt(217/2) Add 5 to both sides: Answer: | | x = 5+sqrt(217/2) or x = 5-sqrt(217/2)
