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Sagot :
Two methods Fred could use to solve the equation are
- The completing the square method
- The formula method
The solution for the function is x ≅ -0.7 OR x ≅ - 3.3
Solving quadratic equations
From the question, we are to solve the given quadratic equation
Two methods Fred could use to solve the equation are
- The completing the square method
- The formula method
The given quadratic function is
f(x) = 4x² + 16x+9
Now, we are to solve f(x) = 0 for x
That is,
4x² + 16x+9 = 0
Using the formula method to solve the equation
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the equation,
a = 4, b = 16, and c = 9
∴ [tex]x =\frac{-16 \pm \sqrt{16^{2}-4(4)(9) } }{2(4)}[/tex]
[tex]x =\frac{-16 \pm \sqrt{256-144 } }{8}[/tex]
[tex]x =\frac{-16 \pm \sqrt{112 } }{8}[/tex]
[tex]x =\frac{-16 \pm 10.58 }{8}[/tex]
[tex]x =\frac{-16+ 10.58 }{8}[/tex] OR [tex]x =\frac{-16- 10.58 }{8}[/tex]
[tex]x =\frac{-5.42 }{8}[/tex] OR [tex]x =\frac{-26.58 }{8}[/tex]
x = -0.6771 OR x = - 3.3229
x ≅ -0.7 OR x ≅ - 3.3
Hence, the solution for the function is x ≅ -0.7 OR x ≅ - 3.3
Learn more on Solving quadratic equations here: https://brainly.com/question/8649555
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