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OverLord2011 [107]
4 years ago
14

How do I solve 7x² - 20x = 3?

Mathematics
1 answer:
Leni [432]4 years ago
5 0

Answer:

3, -1/7

Step-by-step explanation:

Use the quadratic formula to solve this problem. First make all terms equal to 0, so subtract 3 from both sides of the equation.

7x^2 - 20x - 3 = 0

Substitute the a, b, and c values into the quadratic formula: \frac{-b\pm\sqrt{b^2-4ac} }{2a}. In this equation:

  • a = 7
  • b = -20
  • c = -3

\frac{-(-20)\pm\sqrt{(-20)^2-4(7)(-3)} }{2(7)}

Simplify this expression until you get to where you have to split the expression off into a positive and negative case.

\frac{20\pm\sqrt{400-4(-21)} }{14}\rightarrow \frac{20\pm\sqrt{400+84} }{14}\rightarrow \frac{20\pm\sqrt{484} }{14}

Now split this into + and -:

\frac{20\pm\sqrt{484} }{14} ~~becomes~~\frac{20+\sqrt{484} }{14} ~~or~~\frac{20-\sqrt{484} }{14}

Solve the positive case first.

\frac{20+\sqrt{484} }{14} \rightarrow \frac{20+22}{14} \rightarrow\frac{42}{14} =\boxed{3}

Solve the negative case next.

\frac{20-\sqrt{484} }{14} \rightarrow\frac{20-22}{14} \rightarrow\frac{-2}{14} = \boxed{-\frac{1}{7} }

These are the two solutions to the quadratic equation.

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