If we do this correctly....we will arrive at a familiar formula....let's see...
ax^2+bx+c=0 subtract c from both sides
ax^2 + bx = -c divide through by a
x^2 +(b/a)x = -c/a complete the square on x
x^2 + (b/a)x + [b^2] / [4a^2] = -c/a + [b^2] / [4a^2] factor the right side....get a common denominator on the left
[x + (b/2a)]^2 = [b^2 - 4ac] / [4a^2] take the square roots of both sides
x + (b/2a) = ±√[b^2 - 4ac]/[2a] subtract (b/2a) from both sides
x = (-b±√[b^2 - 4ac]) / [2a]
Voila!!!....we have the Quadratic Formula..... !!!!
If we do this correctly....we will arrive at a familiar formula....let's see...
ax^2+bx+c=0 subtract c from both sides
ax^2 + bx = -c divide through by a
x^2 +(b/a)x = -c/a complete the square on x
x^2 + (b/a)x + [b^2] / [4a^2] = -c/a + [b^2] / [4a^2] factor the right side....get a common denominator on the left
[x + (b/2a)]^2 = [b^2 - 4ac] / [4a^2] take the square roots of both sides
x + (b/2a) = ±√[b^2 - 4ac]/[2a] subtract (b/2a) from both sides
x = (-b±√[b^2 - 4ac]) / [2a]
Voila!!!....we have the Quadratic Formula..... !!!!