Activity 2: Give me my reasons! Using your knowledge in solving quadratic equations by completing the squares, give the reason of every step below. Choose your answers from the box below. You can revisit the previous topic in answering this activity. Steps 1. ax²+bx+c=0 b - 2. x2 + x = Ronsons Standard from 2. ** ++ ++ (x + 2 4. 2-4ad 5. (x + 2) = 101-400 b20 6: a 1 20 -bb- 20 7. Quadratic Formula Express the perfect trinomial to square of binomials Divide both sides by a Odrate Formula Extract both sides. Add on both side of the equation Find the value of
Answers & Comments
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.