[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]
[tex] x=3[/tex] or [tex]x=-6 [/tex]
[tex]\pink{===========================>} [/tex]
add 18 no both side of the equation then simplify
[tex] {x}^{2} + 3x - 18 = 0[/tex][tex] {x}^{2} + 3x - 18 + 18 = 0 + 18[/tex]
⠀⠀⠀⠀⠀[tex] {x}^{2} + 3x = 18[/tex]
add to both sides of the equation the square of ane-half of 3
[tex] \boxed{\frac{1}{2} (3) = \frac{3}{2} - > ( \frac{3}{2} {)}^{2} = \frac{9}{4}} [/tex]
[tex] {x}^{2} + 3x = 18 [/tex]
[tex] {x}^{2} + 3x + \frac{9}{4} = 18 + \frac{9}{4} [/tex]
[tex] {x}^{2} + 3x + \frac{9}{4} = \frac{74}{4} + \frac{9}{4} [/tex]
[tex] {x}^{2} + 3x + \frac{9}{4} = \frac{18}{4} [/tex]
expess [tex] {x}^{2} + 3x + \frac{9}{4} [/tex]as a square of binomial
[tex] {x}^{2} + 3x + \frac{9}{4} = \frac{18}{4} - > (x + \frac{3}{2} {)}^{2} = \frac{81}{4} [/tex]
Solve[tex](x + \frac{3}{2} {)}^{2} = \frac{81}{4}[/tex] by extracting the square root
[tex](x + \frac{3}{2} {)}^{2} = \frac{81}{4} - > x ± \frac{3}{2} = + \sqrt{ \frac{81}{4} }[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀[tex]x ± \frac{3}{2} = + \frac{9}{2} [/tex]
[tex]\pink{===========================>} [/tex]
[tex]\boxed{x + \frac{3}{2}= \frac{3}{2} }[/tex]
[tex]\boxed{x + \frac{3}{2} - \frac{3}{2 } = \frac{9}{2} - \frac{3}{2}}[/tex]
[tex]\boxed{x =\frac{6}{2}}[/tex]
[tex]\boxed{x=3} [/tex]
[tex]\pink{===========================>} [/tex]
[tex]\boxed {x + \frac{3}{2} = - \frac{9}{2}} [/tex]
[tex]\boxed {x + \frac{3}{2} - \frac{3}{2 } = \frac{9}{2} - \frac{3}{2}}[/tex]
[tex]\boxed{x =-\frac{12}{2}}[/tex]
[tex]\boxed{x=-6 }[/tex]
[tex]\pink{===========================>} [/tex]
[tex]\colorbox{lightyellow}{CarryOnLearning}[/tex]