goldyprincess227
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.