Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

x^2 - 4x = 5
A) 11,-7
B) 1.73,-1.73
C) 5,-1
D) 1,3

Answer 1

C

Explanation:

Step 1, the coefficient of x is -4

Step 2, divide it by 2= -2

Step 3, square your answer and add to both sides

Square of -2 is 4, and we add to both sides of the equation to give,

x^2 - 4x + 4 = 5 +4

X^2 +4 = 9

(x +2)^2 = 9

take the sqrt of both sides, we have

X +2 = sqrt (9)

X = 2(+ or -) Sqrt (9)

X = 2+ Sqrt (9), 2-sqrt (9)

X = 2+3, 2-3

X= 5, -1

Answer 2

C) 5,-1

Explanation:

Given equation is
`\[x^(2)-4x=5\]`

Expressing the equation equivalently,

`\[x^(2)-4x-5=0\]`

`\[=> x^(2)-5x+x-5=0\]`

`\[=> x*(x-5)+1*(x-5)=0\]`

`\[=> (x-5)*(x+1)=0\]`

Hence the solutions of this equation can be represented as x-5=0 and x+1=0

In other words, x=5 or x=-1

Among the given options, option C is the correct one.