ax^2+bx+c=0

Question

In this question you have to complete the square, but i am confused becuase it is all letters.

Answer 1

ax² + bx + c = 0

x² + bx/a + c/a = 0                          divide both sides by a

x² + bx/a + (b/2a)² + c/a = (b/2a)²    complete the square

(x + b/2a)² + c/a = b²/4a²                left side as square

(x + b/2a)² = b²/4a² - c/a                 subtract c/a from both sides

(x + b/2a)² = b²/4a² - 4ac/4a^{2             LCD}

(x + b/2a)² = (b² - 4ac) / 4a²               combine

x + b/2a = ±√(b² - 4ac) / 2a            take square root

x = (-b ± ±√(b² - 4ac)) / 2a             subtract b/2a form both sides

 

OMG it's the Quadratic Formula!