Question

What are the steps to solve 2x^2+5x-12=0

Answer 1

In order to solve a quadratic equation, the first step is identifying the parameters a, b and c of the standard form:

`\begin{gathered} ax^2+bx+c=0\\ \\ 2x^2+5x-12=0\\ \\ a=2,\text{ }b=5,\text{ }c=-12 \end{gathered}`

Now, the next step is using the quadratic formula to find the values of x:

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a)\\ \\ x=(-5\pm√(5^2-4\cdot2\cdot(-12)))/(2\cdot2)\\ \\ x=(-5\pm11)/(4)\\ \\ x_1=(-5+11)/(4)=(6)/(4)=1.5\\ \\ x_2=(-5-11)/(4)=(-16)/(4)=-4 \end{gathered}`

Therefore the solutions are x = 1.5 and x = -4.