Answer:
[tex]\boxed{\boxed{\sf x=\frac{\sqrt{217} +2}{3} }\:or\: {\sf\boxed{\sf x=\frac{2-\sqrt{217} }{3} } }}[/tex]
Step-by-step explanation:
[tex]\boxed{\sf Quadratic \:equation}[/tex]
*All equations of the form ax^2+bx+c=0 can be solved using the Quadratic Formula. *
[tex]\boxed{\sf \square \: \:\frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The Quadratic Formula gives two solutions, one when ± is addition and one when its subtraction.
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[tex]\boxed{\sf 3x^2-4x-71=0}[/tex]
This equation here is in the standard form: ax^2+bx+c=0.
Substitute 3 → a, -4 → b, -71 → c.
[tex]\sf x=\cfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\times \:3\left(-71\right)}}{2\times \:3}[/tex]
→ Square -4, and then multiply -4 × 3= :
[tex]x=\cfrac{-(-4)\pm \sqrt{16+12(-71)} }{2\times 3}[/tex]
Multiply -12 × -71 = 868, then Add 16+852= 868
[tex]\sf x=\cfrac{-(-4)\pm 2\sqrt{217} }{2\times 3}[/tex]
Take the Square root of 868 2√(217).
* the opposite of -4 → 4.
[tex]\sf x=\cfrac{4\pm 2\sqrt{217} }{2\times 3}[/tex]
Multiply 2 × 3 = 6
[tex]\sf x=\cfrac{4\pm 2\sqrt{217} }{6}[/tex]
Now, we'll solve the equation when ± is plus.
→ Add 4+ 2√(217).
→ Divide 4+ 2√(217 ) by 6.
[tex]\boxed{\sf x=\frac{\sqrt{217} +2}{3} }[/tex]
Now, we'll solve the equation when ± is minus.
→ Subtract 2√(217) from 4.
→ Divide 4 - 2√(217) by 6.
[tex]\boxed{\sf x=\frac{2-\sqrt{217} }{3} }[/tex]
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