Question

What are the solutions of 4x2 + x = –3?

Answer 1

\[4x ^{2}+x+3=0 \it has no real solution,do you want complex solutions.\]

Answer 2

yes

Answer 3

\[4x ^{2}+x=-3\]
\[x ^{2}+\frac{ 1 }{ 4 }x=-\frac{ 3 }{ 4 }\]
\[add both sides (\frac{ co-efficient of x }{ 2 })^{2} i.e.,\left( \frac{ 1 }{ 8 } \right)^{2} or \frac{ 1 }{64 }\]
and complete the squares and find the two values of x.

Answer 4

followed or should i solve further.

Answer 5

I am confused on how to complete the square

Answer 6

you can also use quadratic formula,otherwise isolve further.
\[x ^{2}+\frac{ 1 }{ 4 }x+\frac{ 1 }{ 64 }=\frac{ -3 }{4 }+\frac{ 1 }{64 }\]
\[\left( x+\frac{ 1 }{ 8 } \right)^{2}=\frac{ -48+1 }{64 }=\frac{ -1*47 }{64 }=\frac{\iota ^{2} 47 }{ 64 }\]
\[x+\frac{ 1 }{ 8 }=\pm \iota \frac{ \sqrt{47} }{ 8 },\]
\[x=\frac{ 1+\iota \sqrt{47} }{8 },x=\frac{ 1-\iota \sqrt{47} }{8 }\]