Question

solve the equation(I was trying to solve this myself, also used some apps to check my work. I use quadratic formula and get a negative square root. can't we just use imaginary numbers? or Is the app correct by saying it's undefined?)

Answer 1

Given:

The equation is given as x²+4x = -13.

The objective is to solve the quadratic formula.

Step-by-step explanation:

The equation can be rewritten as,

`x^2+4x+13=0\text{ . . . . . . (1)}`

Consider the coefficients of the equation as,

`\begin{gathered} a=1 \\ b=4 \\ c=13 \end{gathered}`

To find solution:

The quadratic formula to find the solutions is,

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\text{ . . . . . .(1)}`

On plugging the obtained values in equation (1),

`\begin{gathered} x=\frac{-4\pm\sqrt[]{(-4)^2-4(1)(13)}}{2(1)} \\ x=\frac{-4\pm\sqrt[]{16-52}}{2} \\ x=\frac{-4\pm\sqrt[]{-36}}{2} \end{gathered}`

Since, the discriminant is less than 1, the solutions will be complex roots.

`\sqrt[\square]{(-1)}=i`

On further solving the above equation,

`\begin{gathered} x=(-4\pm6i)/(2) \\ x=(-4)/(2)\pm(6i)/(2) \\ x=-2\pm3i \\ x=-2+3i,-2-3i \end{gathered}`

Hence, the solutions of the equation are (-2+3i) and (-2-3i).