Question

4n² +7n=0 what do I do if there is no part c?

Answer 1

• Find the coefficients using ax^2 + bx + c = 0

a = 4

b = 7

c = 0

• Make the coefficient equal 1. But how do we do that? Division.

4n² + 7n = 0

4/4n² + 7n/4 = 0/4

• Simplify

= n² + 7/4n = 0

a = 1

b = 7/4

c = 0

• Complete the square using b/2².

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

• Solve for the unknown x

`(n+(7)/(8))^2=(49)/(64)\\\sqrt{(n+(7)/(8))^2}=\sqrt{(49)/(64)}\\`

Next, cancel out the square on the left side.

`n+(7)/(8)=+/-\sqrt{(49)/(64)}`

Subtract 7/8 from both of the sides.

`n+(7)/(8)-(7)/(8)=-(7)/(8)+/-\sqrt{(49)/(64)}`

Simplify the left side.

`n=-(7)/(8)+/-\sqrt{(49)/(64)}\\n=-(7)/(8)+/-(√(49))/(√(64))\\n=-(7)/(8)+/-(7)/(8)\\n_1=0\\n_2=-(7)/(4)`

That wraps it up for this equation. Hope it helped!