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

Question

asked Mar 11, 2023 145k views

1 Answer

TAGraves · Answer 1 · 2023-03-16T05:39:19+0000

Answer:

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
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:

$\implies x=4\pm√(4 \cdot 3)$

$\implies x=4\pm√(4)√(3)$

$\implies x=4\pm2√(3)$