Answer:
Step 6 is missing the fact that the left hand side is raised to the second power.
Step-by-step explanation:
First cancel c from the left hand side by subtracting it from each side:
ax²+bx+c = 0
ax²+bx+c-c = 0-c
ax²+bx = -c
Next cancel a from the left hand side by dividing all terms by a:
ax²/a + bx/a = -c/a
x² + (b/a)x = -c/a
Next we will complete the square. We do this by dividing the second coefficient, b/a, by 2 and then squaring it; (b/a)÷2 = b/2a; (b/2a)² = b²/4a²
Add this to each side:
x²+(b/a)x+(b²/4a²) = -c/a + (b²/4a²)
Next we will find a common denominator on the right hand side. To do this, multiply the first term by 4a (to make the denominator 4a²):
x²+(b/a)x+(b²/4a²) = (-c*4a)/(a*4a) + (b²/4a²)
x²+(b/a)x+(b²/4a²) = -4ac/4a² + b²/4a²
We can write the left hand side as a squared binomial:
(x+b/2a)² = (b²-4ac)/4a²
Take the square root of both sides:
√(x+b/2a)² = √((b²-4ac)/4a²)
x+b/2a = √(b²-4ac)/2a
Subtract b/2a from each side:
x+b/2a - b/2a = √(b²-4ac)/2a - b/2a
x = (-b ± √(b²-4ac))/2a
