Firstly we learn the standard quadratic equation,
ax²+bx+c=0
where a,b,c are real numbers.
Now solve the quadratic equation using the Complete the square method.
Rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax² + bx + c = 0 and then solve for x,
ax²+bx=-c
x² + [tex] \frac{b}{a} x [/tex]=-c
add both the side [tex] (\frac{b}{2a} )^{2} [/tex]
x² + [tex] \frac{b}{a} x [/tex]+[tex] (\frac{b}{2a})^{2} = -\frac{c}{a} + (\frac{b}{2a})^{2} [/tex]
[tex] (x+\frac{b}{2a})^{2} = \frac{b^{2}-4ac}{4a^{2}} [/tex]`
take square root both the side
[tex] x = \frac{-b+\sqrt{b^{2}-4ac}}{2a} [/tex]
[tex] x= \frac{-b-\sqrt{b^{2}-4ac}}{2a} [/tex]
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.
Step-by-step explanation:
:)
