Question

In order to solve 7x² + 5x - 3 = 0 by the quadratic formula

Answer 1

We can solve a quadratic equation of the form:

`ax^2+bx+c=0`

The quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

Given the equation:

`\begin{gathered} 7x^2+5x-3=0 \\ a=7,b=5,c=-3 \end{gathered}`

Therefore:

`\begin{gathered} x=(-5\pm√(5^2-4*7*-3))/(2*7) \\ =(-5\pm√(25-(-84)))/(14) \\ =(-5\pm√(25+84))/(14) \\ =(-5\pm√(109))/(14) \\ \text{Therefore:} \\ x=(-5+√(109))/(14)\lor x=(-5-√(109))/(14) \\ x=0.3886\lor x=-1.1029 \end{gathered}`