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

Number 43 is the one problem that I need some guidance with. Solve each equation with-example-1
User Ppeterka
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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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User Johnnymnmonic
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