[tex] {2x}^{2} + 3x = - 1 [/tex]
add 1 to both sides
[tex]{2x}^{2} + 3x + 1 = 0[/tex]
plug in for the formula
[tex] {ax}^{2} + bx + c[/tex]
[tex] \frac{ - b + ( - ) \sqrt{ {b}^{2} - 4(a)(c) } }{2(a)} [/tex]
[tex] \frac{ - 3 + ( - ) \sqrt{ {3}^{2} - 4(2)(1) }}{2(2)} [/tex]
simplify by multiplying and exponents
[tex] \frac{ - 3 + ( - ) \sqrt{ 9 - 8 }}{4} [/tex]
subtract then solve the square root
[tex]\frac{ - 3 + ( - ) \sqrt{ 1}}{4} [/tex]
[tex]\frac{ - 3 + ( - ) 1}{4} [/tex]
now solve for the plus and minus
(plus):
[tex]\frac{ - 3 + 1}{4} [/tex]
[tex] \frac{ - 2}{4} = - 0.5[/tex]
(minus):
[tex]\frac{ - 3 - 1}{4} [/tex]
[tex] \frac{ - 4}{4} = - 1[/tex]
so the answer would be -0.5 and -1
