Answer:
[tex]x=4+2\sqrt{3}[/tex]
[tex]x=4-2\sqrt{3}[/tex]
Step-by-step explanation:
Completing the square
when [tex]ax^2+bx+c=0[/tex]
Given equation:
[tex]3x^2-24x+40=28[/tex]
Subtract 40 from both sides:
[tex]\implies 3x^2-24x=-12[/tex]
Divide both sides by 3:
[tex]\implies x^2-8x=-4[/tex]
Add the square of half the coefficient of [tex]x[/tex] to both sides:
[tex](\frac{b}{2})^2=(\frac{-8}{2})^2=16[/tex]
[tex]\implies x^2-8x+16=-4+16[/tex]
Factor the left side and simplify the right side:
[tex]\implies (x-4)^2=12[/tex]
Square root both sides:
[tex]\implies x-4=\pm\sqrt{12}[/tex]
Add 4 to both sides and simplify the radical:
[tex]\implies x=4\pm\sqrt{4 \cdot 3}[/tex]
[tex]\implies x=4\pm\sqrt{4}\sqrt{3}[/tex]
[tex]\implies x=4\pm2\sqrt{3}[/tex]
