3
x2+24x+144 = 9 x2+24x+144-9 = 0 x2+24x+135 = 0 (x+9)(x+15) = 0 x = -9 or x = -15
x2 + 7x + 9 = 3 ∴ x2 + 7x + 6 = 0 ∴ (x + 6)(x + 1) = 0 ∴ x ∈ {-6, -1}
x2 + 6x + 9 = 81 x2 + 6x = 72 x2 + 6x - 72 = 0 (x+12)(x-6) = 0 x= -12, 6 (two solutions)
-171 = 19x so x = -9
9 needs to be added to complete the square. When squaring (x + n), the result is x2 + 2nx + n2. We have +10x, so n must be 10/2 = 5. Thus: (x + 5)2 = x2 +10x + 25 = x2 +10x + 14 + 9 So 9 needs to be added to complete the square, giving: x2 +10x + 14 = (x + 5)2 - 9
Complete the squares: x2 - 10x + 25 + y2 + 4y + 4 - 52 = 25 + 4 = 29 x2 - 10x + 25 + y2 + 4y + 4 = 52 + 29 = 81 So the radius is sqrt(81) = 9
(x+1)(x+9)
0
(3,21)
x = 4
5x + 4 = 10x - 5 10x - 5x = 4 + 5 5x = 9 x = 1.8
x2 + y2 - 10x + 4y - 52 = 0 x2 - 10x + y2 + 4y = 52 Complete the square (x2 - 10x + 25) + (y2 + 4y + 4) = 52 + 25 + 4 (x - 5)2 + (y + 2)2 = 81 (x - 5)2 + (y - -2)2 = 92 This is the equation of a circle with center (5, -2), and radius 9.
Type your answer here. Find the radius for a circle with the equation x2 plus y2 equals 9? ..
X2 or 2 times x?
-10x+3 = -x+12 -10x+x = 12-3 -9x = 9 x = -1
(x+1)(x+9)