Answer:
a = 4
b = 7
c = 0
4n² + 7n = 0
4/4n² + 7n/4 = 0/4
= n² + 7/4n = 0
a = 1
b = 7/4
c = 0
b = 7/4
(b/2)² = (7/4 ÷ 2)²
Use fraction rule.
7/4 ÷ 2² = 7/4² / 2²
square the numbers
7/4² / 2² = 49/16 ÷ 4
49/16 ÷ 4 = 49/16 × 1/4
49/16 × 1/4 = 49/64
Add to both sides of the equation using 49/64
b = 7/4
b/2 = 7/4 ÷ 2
simplify
b/2 = 7 ÷ (4 × 2)
simplify(arithmetic)
b/2 = 7/8
n² + 7/4n + 49/64 = 49/64
(n + 7/8)² = 49/64
[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]
Next, cancel out the square on the left side.
[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]
Subtract 7/8 from both of the sides.
[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]
Simplify the left side.
[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]
That wraps it up for this equation. Hope it helped!
