Rearrange: x2 - 10x + 25 = 0ie (x - 5)(x - 5) = 0x = 5Check: x2 = 25; 10x - 25 = 50 - 25 = 25. Job done
10x - 5 = 2510x = 30x = 3
-20
y=x2-10x+30=(x-5)2-25+30=(x-5)2+5
x2 + 10x + 25 = 0
Rearrange: x2 - 10x + 25 = 0ie (x - 5)(x - 5) = 0x = 5Check: x2 = 25; 10x - 25 = 50 - 25 = 25. Job done
For the equation x2- 10x - k equals 0, you can solve this by knowing that if there is only one solution then the discriminant b2 - 4ac must be equal to 0. In this equation, a is 1, b is 10 and c is k This equation becomes 100 - 4k equals 0, and k is 25.
10x = 9x -25 10x -9x = -25 x = -25
x2 + 10x = 18 x2 + 2(5)x - 18 = 0 x2 + 2(5)x + 25 = 18 + 25 (x + 5) 2 = 43 x + 5 = 430.5 x=6.56(3sf)-5
When x = -5
15
Using the quadratic equation formula: x = -5-/+ the square root of 7
10x - 5 = 2510x = 30x = 3
-20
y=x2-10x+30=(x-5)2-25+30=(x-5)2+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.
x2 + 10x + 25 = 0