Question

If ax*x + bx + c = 0, then what is x?

Answer 1

ax² + bx + c = 0

divide the equation by a

x² + (b/a)x + c/a = 0

[x+(b/2a)]² -b²/4a² + c/a = 0

[x+(b/2a)]² - (b² - 4ac)/4a² = 0

[x+(b/2a)]² - [√(b² - 4ac)/√4a²]² =0

[x+(b/2a)]² - [√(b² - 4ac)/2a]² =0

{ x + b/2a + √(b² - 4ac)/2a }{ x + b/2a - √(b² - 4ac)/2a } = 0

{ x + [b+ √(b² - 4ac)]/2a }{ x + [b- √(b² - 4ac)]/2a } = 0

x = [-b - √(b² - 4ac)]/2a or x = [-b + √(b² - 4ac)]/2a

x = [-b ± √(b² - 4ac)]/2a