Question

Describe and justify the methods you used to solve the quadratic equations in parts A and B. A and b are the problems in the picture.

Answer 1

We are asked to justify the method and solve the given quadratic equations.

Part A:

`2x(x+1.5)=-1`

Let us solve the above quadratic equation using the quadratic formula

First, expand the equation to convert it into the standard form.

`\begin{gathered} 2x(x+1.5)=-1 \\ 2x^2+3x=-1 \\ 2x^2+3x+1=0 \end{gathered}`

So, the coefficients of the quadratic equation are

a = 2

b = 3

c = 1

The quadratic formula is given by

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ x=\frac{-3\pm\sqrt[]{3^2-4(2)(1)}}{2(2)} \\ x=\frac{-3\pm\sqrt[]{9^{}-8}}{4} \\ x=\frac{-3\pm\sqrt[]{1}}{4} \\ x=(-3\pm1)/(4) \\ x=(-3+1)/(4),\; (-3-1)/(4)\; \\ x=(-2)/(4),\; (-4)/(4)\; \\ x=-0.5,\; -1\; \end{gathered}`

Therefore, the solution is x = -0.5 and x = -1