Question

Number 43 is the one problem that I need some guidance with. Solve each equation with the quadratic formula.

Answer 1

Question 43.

Given the equation:

`12x^2-8x-9=0`

Let's solve using the quadratic formula.

Apply the quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

Use the standard formula to find the values of a, b and c:

`\begin{gathered} ax^2+bx+c=0 \\ 12x^2-8x-9=0 \end{gathered}`

Where:

a = 12

b = -8

c = -9

Input values into the quadratic formula and solve for x:

`\begin{gathered} x=(-(-8)\pm√((-8)^2-4(12)(-9)))/(2(12)) \\ \\ x=(8\pm√(64-(-432)))/(24) \\ \\ x=(8\pm√(64+432))/(24) \\ \\ x=(8\pm√(496))/(24) \end{gathered}`

Solving further:

`\begin{gathered} x=(8\pm√(31*16))/(24) \\ \\ x=(8\pm4√(31))/(24) \end{gathered}`

Now, let's simplify:

`\begin{gathered} x=(8)/(24)\pm(4√(31))/(24) \\ \\ x=(1)/(3)\pm(1√(31))/(6) \\ \\ x=(1)/(3)\pm(√(31))/(6) \end{gathered}`

ANSWER:

`x=(1)/(3)\pm(√(31))/(6)`

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