Complete the steps of the derivation of the quadratic formula.
Step 1: (x+b/2a)^2-b^2-4ac/4a^2=0
Step 2: Expand the left side of the equation:
(x^2 + 2bx + b^2)/(4a^2) - b^2 - 4ac/4a^2 = 0
Step 3: Multiply every term by 4a^2 to get rid of the fractions:
x^2 + 2bx + b^2 - 4a^2b^2 - 16ac = 0
Step 4: Rearrange terms to isolate x^2 term:
x^2 + 2bx = 4a^2b^2 + 16ac - b^2
Step 5: Complete the square by adding (b/2a)^2 to both sides:
x^2 + 2bx + (b/2a)^2 = 4a^2b^2 + 16ac - b^2 + (b/2a)^2
Step 6: Factor the left side:
(x + b/2a)^2 = 4a^2b^2 + 16ac - b^2 + b^2/4a^2
Step 7: Simplify the right side:
(x + b/2a)^2 = 4a^2b^2 + 16ac
Step 8: Take the square root of both sides:
x + b/2a = ±√(4a^2b^2 + 16ac)
Step 9: Simplify further:
x = (-b ± √(b^2 - 4ac))/(2a)
This is the quadratic formula.