goldyprincess227
Answered

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Solve the quadratic equation x2 - 12x + 23 =0 by completing the square.
A) x = 13 6
B) x = 13 - 6
C) x = -6 13
D) x= 6 13

Sagot :

Answer:

Completing the square is always confusing, but if you keep in mind it's just a way to write  (A + B )^2  so that the problem is in some easier form it makes a bit better sense.  A perfect square has some helpful properties.. anyway..

Step-by-step explanation:

Given: [tex]x^{2}[/tex] - 12x +23 = 0   ( not a perfect square , tough to work with )

take 1/2 of the second term  coefficient  12/2 = 6   and square it

[tex]x^{2}[/tex] - 12x + ([tex]-6)^{2}[/tex] +23 = [tex](-6)^{2}[/tex]

[tex]x^{2}[/tex] -12x + [tex]6^{2}[/tex] +23 = [tex]6^{2}[/tex]

now there is a perfect square :)

(x - 6)^2 =36-23

(x - 6)^2 = 13

take the square root of both side now

x -6 = [tex]\sqrt{13}[/tex]

x = [tex]\sqrt{13}[/tex] +6

sooo  what is supposed to happen in these problems  is that square root of 13 is supposed to work out to something that is easy to find the root of ... maybe in your answers you left out the square roots?   so maybe A is right  :/

facundo3141592

We want to solve a quadratic equation by completing squares.

What we need to use is the general relation:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

We will see that the solutions are:

[tex]x = 6 \pm \sqrt{13}[/tex]

We start with the equation:

[tex]x^2 - 12x + 23 = 0\\[/tex]

We can rewrite the middle term as:

[tex]x^2 - 2*6*x + 23 = 0\\[/tex]

Now remember that 6*6  = 36

Then we can add 13 and subtract 13 to get:

[tex]x^2 - 2*6*x + 23 + 13 - 13 = 0\\x^2 - 2*6*x + 36 - 13 = 0\\x^2 - 2*6*x + (-6)^2 - 13 = 0\\(x - 6)^2 - 13 = 0[/tex]

Then the solutions are:

[tex](x - 6) = \pm \sqrt{13} \\\\x = 6 \pm \sqrt{13}[/tex]

If you want to learn more, you can read:

https://brainly.com/question/17177510

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