Question

How do I solve 7x² - 20x = 3?

Answer 1

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.