Given equation:
[tex]5x^2-7x\text{ = 2}[/tex]
Re-arranging:
[tex]5x^2-7x\text{ -2 = 0}[/tex]
Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]
a = 5, b = -7, c= -2
Substituting into the formula:
[tex]\begin{gathered} x\text{ = }\frac{-(-7)\pm\text{ }\sqrt[]{(-7)^2-4(5)(-2)}}{2\times5} \\ =\text{ }\frac{7\pm\sqrt[]{89}}{10} \end{gathered}[/tex]
Writing as a decimal:
[tex]x\text{ = }-0.24\text{ or 1.64 (nearest hundredth)}[/tex]
Answer:
x = -0.24, 1.64
