Assignment: [tex]\bold{Solve \ Equation: \ 3x^2+15x=18}[/tex]
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Answer: [tex]\boxed{\bold{x=1,\:x=-6}}[/tex]
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Explanation: [tex]\downarrow\downarrow\downarrow[/tex]
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[ Step One ] Subtract 18 From Both Sides
[tex]\bold{3x^2+15x-18=18-18}[/tex]
[ Step Two ] Simplify
[tex]\bold{3x^2+15x-18=0}[/tex]
[ Step Three ] Solve With Quadratic Formula
Note: [tex]\bold{For\:a\:quadratic\:equation\:of\:the\:form\: ax^2+bx+c=0}[/tex]
[tex]\bold{the \ solutions \ are \ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\bold{a=3,\:b=15,\:c=-18:\quad x_{1,\:2}=\frac{-15\pm \sqrt{15^2-4\cdot \:3\left(-18\right)}}{2\cdot \:3}}[/tex]
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[tex]\bold{\frac{-15+\sqrt{15^2-4\cdot \:3\left(-18\right)}}{2\cdot \:3}: \ 1}[/tex]
[tex]\bold{\frac{-15-\sqrt{15^2-4\cdot \:3\left(-18\right)}}{2\cdot \:3}: \ -6}[/tex]
[ Step Four ] Combine Solutions
[tex]\bold{x=1,\:x=-6}[/tex]
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[tex]\bold{\rightarrow Mordancy \leftarrow}[/tex]
Answer: x1=1
x2=-6
Step-by-step explanation:
3x^2+15x-18=0
D^2=225-4*3*(-18)/6=411
D=21
x1=(-15+21)/6=1
x2=(-15-21)/6=-6
