Answer:
Step-by-step explanation:
3x²=15-4x
divide by 3 on both sides
x²=5-[tex]\frac{4}{3}[/tex]x
move everything to one side
x²+[tex]\frac{4}{3}[/tex]x -5 = 0
add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex] but also subtract it too
x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]-5-[tex]( \frac{2}{3} )^{2}[/tex] = 0
now use the property of a perfect square to rewrite
[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0
rewrite 5 as a fraction
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0
add up the fractions
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0
move to the other side
[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]
take the square root of both sides :P
[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex] = [tex]\sqrt{\frac{49}{9} }[/tex]
much easier looking now, just use algebra to solve for x
x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
subtract [tex]\frac{2}{3}[/tex] from both sides
x + [tex]\frac{2}{3}[/tex] - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{3}[/tex]
:)
