(x-7)(x-3)
x2 + 10x = 0 x2 + 10x + 25 = 25 (x + 5)2 = 25 x + 5 = +-5 x1 = 0 x2 =10
x2 - 10x + 25 = 0(x - 5)(x - 5) = 0x - 5 = 0x = 5
-5
Given: x2 + y2 - 10x + 4y + 4 = 0 First, we'll move our constants to the right: x2 + y2 - 10x + 4y = -4 Then group terms with the same variables together: x2 - 10x + y2 + 4y = -4 Then complete the squares: x2 - 10x + 25 + y2 + 4y + 4 = -4 + 25 + 4 (x - 5)2 + (y + 2)2 = 25 And there we have it. This is an equation for a circle whose center point is at (5, -2), with a radius of √25, which equals 5.
(x-7)(x-3)
x2 + 10x + 25 --> (x + 5)2
x2 + 10x = 0 x2 + 10x + 25 = 25 (x + 5)2 = 25 x + 5 = +-5 x1 = 0 x2 =10
Given: x2 + 10x - 16 Let: x2 + 10x - 16 = 0 x2 + 10x - 16 = 0 ∴ x2 + 10x + 25 = 16 + 25 ∴ (x + 5)2 = 41 ∴ x = -5 ± √41 ∴ x2 + 10x - 16 = (x + 5 + √41)(x + 5 - √41)
Twenty-Five x2 + 10x = 8 x2 + 10x + 25 = 8 + 25 (x + 5)2 = 33
Rearrange: x2 - 10x + 25 = 0ie (x - 5)(x - 5) = 0x = 5Check: x2 = 25; 10x - 25 = 50 - 25 = 25. Job done
x2 - 10x + 25 = 64 Or x2 - 10x + 25 = 64? If the first, move all over to 1 side; x2 - 10x + 25 - 64 = 0 x2 - 10x + -39 = 0 Then make it into quadratic equations; (x - 13)(x + 3) = 0 Therefore x = 13 or x = -3. If the second, 8x = -39 -39/8 = -9.75 = x
x2 - 10x + 25 = 0(x - 5)(x - 5) = 0x - 5 = 0x = 5
depends on what x is
This can be factored in multiple ways, depending on the signs. X2+10x+25 factors into (x+5)2 or (x+5)(x+5). X2-10x+25 factors into (x-5)2 or (x-5)(x-5). If 25 is being subtracted, then the trinomial is impossible to factor.
x2 + 10x + 25 = 0
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