Question

Use completing the square to determine which of the following gives the solutions to 3x2 - 24x + 40 = 28.

A 2+413
O B. 4+2√3
o C. 37312
D. 6+2/5

Answer 1

`x=4+2√(3)`

`x=4-2√(3)`

Explanation:

Completing the square

when
`ax^2+bx+c=0`

Given equation:

`3x^2-24x+40=28`

Subtract 40 from both sides:

`\implies 3x^2-24x=-12`

Divide both sides by 3:

`\implies x^2-8x=-4`

Add the square of half the coefficient of
`x` to both sides:

`((b)/(2))^2=((-8)/(2))^2=16`

`\implies x^2-8x+16=-4+16`

Factor the left side and simplify the right side:

`\implies (x-4)^2=12`

Square root both sides:

`\implies x-4=\pm√(12)`

Add 4 to both sides and simplify the radical:

`\implies x=4\pm√(4 \cdot 3)`

`\implies x=4\pm√(4)√(3)`

`\implies x=4\pm2√(3)`