Step-by-step explanation:
ax
2
+bx+c=0
ax^{2} + bx = cax
2
+bx=c
x^{2} +\frac{b}{a}x = -\frac{c}{a}x
2
+
a
b
x=−
a
c
x^{2} + \frac{b}{a}x + (\frac{b}{2a} )^{2} = -\frac{c}{a} + (\frac{b}{2a} )^{2}x
2
+
a
b
x+(
2a
b
)
2
=−
a
c
+(
2a
b
)
2
(x+\frac{b}{2a} )^{2} = -\frac{c}{a} + \frac{b^{2} }{4a^{2} }= \frac{b^{2} -4ac}{4a^{2} }(x+
2a
b
)
2
=−
a
c
+
4a
2
b
2
=
4a
2
b
2
−4ac
\sqrt{(x+\frac{b}{2a} )^{2} } =\sqrt{\frac{b^{2} -4ac}{4a^{2} }}
(x+
2a
b
)
2
=
4a
2
b
2
−4ac
x+\frac{b}{2a} } = ±\frac{\sqrt{b^{2}-4ac } }{2a}
2a
b
2
−4ac
x = -\frac{b}{2a}x=−
2a
b
±\frac{\sqrt{b^{2}-4ac } }{2a}
2a
b
2
−4ac
Steps:
1. Transpose the constant term to the right side of the equation.
2. Divide both sides by the coefficient of the first term.
3. Divide the quotient of the first and second coefficient by 2, then square the result. Do not forget to add it to the right side of the equation.
4. Rewrite the left side of the equation as a perfect square trinomial.
5. Get the LCD on the right side of the equation and write it as the addition of fractions with similar denominators.
5. Square both sides of the equation.
6. Transpose any term on the left side of the equation.
Solving the said equation will actually lead to the derivation of the Quadratic Formula.
