That is the formula for a circle: complete the squares in x and y to find the centre and the radius:
A circle with centre (x0, y0) and radius r has the formula:
(x - x0)² + (y - y0)² = r²
Completing the square is a technique to convert x² - ax into a perfect square less a constant c, ie:
x² - ax = (x - b)² - c
Now:
(x - b)² = x² - 2bx + b²
→ x² - 2bx = (x - b)² - b²
If b = a/2, this becomes:
x² - ax = (x - a/2)² - (a/2)²
So back to the given equation:
x² + y² - 6x - 10y + 9 = 0
→ (x² - 6x) + (y² - 10y) + 9 = 0
→ ((x -3)² - 3²) + ((y - 5)² - 5²) + 9 = 0
→ (x - 3)² + (y - 5)² + (-9 - 5² + 9) = 0
→ (x - 3)² + (y - 5)² - 5² = 0
→ (x - 3)² + (y - 5)² = 5²
→ It is a circle with centre (3, 5) and radius 5.
X=1
7(3y-2)-(-4y+9)
{-1,7}
By including its plus or minus signs
a2 + 62 = 122 a2 + 62 - 62 = 122 - 62 a2 = 144 - 36 a2 = 108 taking the square root of each side, we get a equal plus or minus the square root of 108, or plus or minus 6 times the square root of 3.
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X=1
Solve using the quadratic formula
hello
x = 25 / 3squared + 5
You have to put your heart into it!
It can be solved by using the quadratic equation formula.
(b-4) squared
2
All the time
I suggest you use the quadratic formula, with a = 3, b = -2, c = 7.
Factor it. (x - 8)(x - 2) x = 2, 8