Answer:
x = 7.5, x = -5
Step-by-step explanation:
1. Plug a(2), b(-5), and c(-75) into the qudratic formula:
[tex]x_{1,2} =\frac{-(-5)+-\sqrt{(-5)^{2}-4(2)(-75) } }{2(2)}[/tex]
2. Find the square:
[tex]x_{1,2} =\frac{-(-5)+-\sqrt{25-4(2)(-75) } }{2(2)}[/tex]
[tex]x_{1,2} =\frac{-(-5)+-\sqrt{25+600} }{2(2)}[/tex]
[tex]x_{1,2} =\frac{-(-5)+-25 }{4}[/tex]
3. Separate the solutions:
[tex]x_{1} = \frac{-(-5)+25}{4} , x_{2} =\frac{-(-5)-25}{4}[/tex]
4. Solve for both:
[tex]x_{1} =\frac{5+25}{4} \\\\x_{1} =\frac{30}{4} \\\\x_{1} =\frac{15}{2}\\\\x_{1} =7.5[/tex]
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[tex]x_{2} =\frac{5-25}{4} \\\\x_{2} =\frac{-20}{4} \\\\x_{2} =-5[/tex]
In conclusion, the solutions are x = 7.5 and -5.
hope this helps!
