Question

What is the negative solution to the equation? 4x² - 12x = 91 A) -3.5 B) -6.5 C) -7 D) -13

Answer 1

We have the following equation

`4x^2-12x=91\Rightarrow4x^2-12x-91=0`

We can solve it using the quadratic formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where, in our problem

a = 4

b = -12

c = -91

Therefore

`\begin{gathered} x=\frac{-(-12)\pm\sqrt[]{(-12)^2-4\cdot4\cdot(-91)}}{2\cdot4} \\ \\ x=\frac{12\pm\sqrt[]{144+16\cdot91)}}{8} \\ \\ x=\frac{12\pm\sqrt[]{144+1456}}{8} \\ \\ x=\frac{12\pm\sqrt[]{1600}}{8} \\ \\ x=(12\pm40)/(8) \end{gathered}`

Now we have the solutions, we only want the negative one, then

`\begin{gathered} x=(12-40)/(8) \\ \\ x=-(28)/(8) \\ \\ x=-3.5 \end{gathered}`

The negative solution of the equation is -3.5, then, the correct answer is the letter A.