Respuesta :

Answer:

The value of x is:

[tex]x=\dfrac{5\pm \sqrt{103}i}{8}[/tex]

Step-by-step explanation:

we have to use the quadratic formula to solve for x.

The equation is given as:

[tex]4x^2-3x+9=2x+1[/tex]

which could also be written as:

[tex]4x^2-3x+9-2x-1=0\\\\4x^2-3x-2x+9-1=0\\\\\\4x^2-5x+8=0[/tex]

The quadratic formula for the quadratic equation of the type:

[tex]ax^2+bx+c=0[/tex] is given as:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

a=4, b=-5 and c=8.

Hence, by the quadratic formula we have:

[tex]x=\dfrac{-(-5)\pm \sqrt{(-5)^2-4\times 8\times 4}}{2\times 4}\\\\x=\dfrac{5\pm \sqrt{25-128}}{8}\\\\\\x=\dfrac{5\pm \sqrt{103}i}{8}[/tex]

Hence, the value of x is:

[tex]x=\dfrac{5\pm \sqrt{103}i}{8}[/tex]

zainebamir540

Answer:

Choice c is the answer.

Step-by-step explanation:

We have given a quadratic equation.

4x²-3x+9 = 2x+1

We have to solve above equation using quadratic formula.

First , Add -2x-1 into both sides of given equation, we have

4x²-3x+9 -2x-1 = 2x+1 -2x-1

Adding like terms, we have

4x²-5x+8  = 0 is general form of quadratic equation, where a = 4, b = -5 and c= 8.

x = (-b±√b²-4ac) / 2a is quadratic formula.

Putting given values in above equation, we have

x = (-(-5)±√(-5)²-4(4)(8) ) / 2(4)

x = (5±√24-128) / 8

x = (5±√-103) / 8

x = (5±√103√-1) / 8          ∴√-1 = i

x = (5±√103i) / 8 Which is the answer.

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