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Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

x^2 - 23 = 10x

a. -1.93, 11.93
b. 1.93, -11.93
c. 1.93, 11.93
d. -1.93, -11.93

Respuesta :

Answer:

Option B. 1.93, -11.93 is the right answer.

Step-by-step explanation:

Here the given equation is x²-23 = 10x and we have to solve the equation for the value of x.

First we simplify the equation to bring in the shape of ax²+bx+c=0

x²-23 = 10x

(x²-23)-10x = 10x-10x

x²-10x -23 = 0

Now we the formula for the value of [tex]x= \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x=\frac{10\pm \sqrt{(-10)^{2}-4(1)(-23)}}{2(1)}[/tex]

[tex]x=\frac{-10\pm  \sqrt{100+92}}{2}[/tex]

[tex]x= \frac{-10\pm \sqrt{192}}{2}[/tex]

[tex]x=\frac{-10\pm 4\sqrt{12}}{2}[/tex]

[tex]x=-5\pm 2\sqrt{12}[/tex] [tex]= -5\pm (2\times 3.464)[/tex] [tex]= -5\pm 6.93[/tex]

Now x = (-5+6.93) = 1.93

and x = (-5-6.93) = -11.93

alinakincsem

Answer:

The correct answer option is a. -1.93, 11.93.

Step-by-step explanation:

We are given the following equation and we are to solve it using the quadratic formula:

[tex]x^2 - 23 = 10x[/tex]

Re-arranging this equation in order of decreasing power:

[tex] x^{2} - 10x - 23 = 0 [/tex]

Using the quadratic formula:

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

Substituting the given values in the formula to get:

[tex]x=\frac{-(-10)+-\sqrt{(-10)^2-4(1)(-23)} }{2(1)}[/tex]

[tex]x=\frac{10+-\sqrt{192} }{2}[/tex]

[tex]x=\frac{10+\sqrt{192} }{2} , x=\frac{10-\sqrt{192} }{2}[/tex]

[tex]x=11.93, x=-1.93[/tex]



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