Question

The steps to derive the quadratic formula are shown below:


Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4


Provide the next step to derive the quadratic formula.

Answer 1

By step 3, the equation reads:
\[x^2 + \dfrac{b}{a}x = -\dfrac{c}{a},\qquad\textrm{with } a \neq 0.\]
In order to derive the quadratic formula, one should now complete the square. That means we should add a suitable term to both sides of the equation so as to use the write the LHS under the form of the square of a binomial, using:
\[(y+z)^2 = y^2 + 2yz + z^2.\]
Can you see what term does just that? \(\ddot{\smile}\)