Derive the Almighty formula explaining each steps in details

The "Almighty formula" refers to the quadratic formula, which solves equations of the form ax^2 + bx + c = 0. Step 1: Start with the standard quadratic equation. ax^2 + bx + c = 0 Step 2: Divide the entire equation by a (assuming a ≠ 0) to make the coefficient of x^2 equal to 1. (ax^2)/(a) + (bx)/(a) + (c)/(a) = (0)/(a) x^2 + (b)/(a)x + (c)/(a) = 0 Step 3: Move the constant term (c)/(a) to the right side of the equation. x^2 + (b)/(a)x = -(c)/(a) Step 4: Complete the square on the left side. To do this, add ((1)/(2) · coefficient of x)^2 to both sides. The coefficient of x is (b)/(a), so we add ((1)/(2) · (b)/(a))^2 = ((b)/(2a))^2 = (b^2)/(4a^2) to both sides. x^2 + (b)/(a)x + ((b)/(2a))^2 = -(c)/(a) + ((b)/(2a))^2 x^2 + (b)/(a)x + (b^2)/(4a^2) = -(c)/(a) + (b^2)/(4a^2) Step 5: Factor the left side as a perfect square. (x + (b)/(2a))^2 = -(c)/(a) + (b^2)/(4a^2) Step 6: Combine the terms on the right side by finding a common denominator, which is 4a^2. (x + (b)/(2a))^2 = -(c)/(a) · (4a)/(4a) + (b^2)/(4a^2) (x + (b)/(2a))^2 = -(4ac)/(4a^2) + (b^2)/(4a^2) (x + (b)/(2a))^2 = (b^2 - 4ac)/(4a^2) Step 7: Take the square root of both sides. Remember to include both positive and negative roots. sqrt((x + (b)/(2a))^2) = ±sqrt((b^2 - 4ac)/(4a^2)) x + (b)/(2a) = ±sqrt(b^2 - 4ac)sqrt(4a^2) x + (b)/(2a) = ±sqrt(b^2 - 4ac)2a Step 8: Isolate x by subtracting (b)/(2a) from both sides. x = -(b)/(2a) ± sqrt(b^2 - 4ac)2a x = -b ± sqrt(b^2 - 4ac)2a The Almighty formula is: x = -b ± sqrt(b^2 - 4ac)2a Send me the next one 📸