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# Factor Completely by COMPLETING THE SQUARE?

Topic: Factor Completely by COMPLETING THE SQUARE?
June 20, 2019 / By Carin
Question: I need help =( so the problem is x^2 - 6x + 8 i got (x-4)(x-2) is that the answer OR do I have to put it into an equation and do x^2-6x= -8 and go from there? AND THE DIRECTIONS SAY FACTOR COMPLETELY (BY COMPLETING THE SQUARE) so, the answer i got (x-4)(x-2) I understand that while deal to get those answers but what method is that called just so I know? and that means that for all the ones that say to complete the square I need to put them in an equation? for example: c^2 - 8c + 15 would start off by being c^2 - 8c = -15 and Id go from there using the complete the square method? so that leaves me with another question. How you said that I can not just put c^2 - 8c + 15 into c^2 - 8c + 15 because it is not mathematically valid how would how do i do the original problem i asked, because it is given to me the same as the c^2 - 8c + 15. it is given x^2 - 6x + 8 without any equal signs. but i have to use the complete the square. But you said its not possible because I cant just put it into x^2 - 6x = -8.

## Best Answers: Factor Completely by COMPLETING THE SQUARE?

Anabella | 1 day ago
Your answer is correct... You just solve the factor, this is not an equation, it´s only an expression...
👍 130 | 👎 1
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Your problem is Solve by completing the square: 10x² + 7x -12 = 0 ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓... The first step, which is often forgot, is to remember the COEFFICIENT OF x² MUST EQUAL ONE before applying the complete the square technique ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓... Therefore divide both sides by TEN this gives x² + (7/10)x - 12/10 = 0 add 12/10 to both sides x² + (7/10)x = 12/10 Now, COMPLETE THE SQUARE by adding the square of 1/2 of 7/10 . Half of 7/10 is 7/20 and the square is 49/400 so we have x² + (7/10)x + 49/400 = 12/10 +49/400 (x + 7/20)² = 480/400 + 49/400 = 529/400 now take the square root of both sides x+ 7/20 = ±√529/ 20 then subtract 7/20 from both sides to obtain x= -7/20±√529/ 20 It turns out that √529 = 23 so x = (-7+ 23)/20 and x = (-7-23)/20 = 16/20 or -30/20 which simplifies to x= 4/5 or x = -3/2

Wayne
You factored properly, but not by completing the square. Here is how you do it: x^2 - 6x + 8 = 0 x^2 - 6x = -8 Take the -6 from the -6x, and divide the -6 by 2. Then square the result. So you get -6/2 = -3, and (-3)^2 = 9. Add this value to both sides of your equation. x^2 - 6x + 9 = -8 + 9 (x - 3)^2 = 1 (x - 3)^2 - 1 = 0 Reason for the following steps: "Take the -6 from the -6x, and divide the -6 by 2. Then square the result. So you get -6/2 = -3, and (-3)^2 = 9. Add this value to both sides of your equation." Notice that (x - a)² = x² - 2ax + a² The term in front of x is 2a Dividing that term by 2 and then squaring gives us the last term we need to make an expression that can be expressed in the form (x - a)² Edit: The way you factored is just called factoring, as far as I know. You would probably not factor by completing the square for most problems unless you are told to. Also, you must be given an equation to solve by completing the square (I am assuming yours was supposed to be set equal to 0). You can't just take c^2 - 8c + 15 and make it an equation by saying c^2 - 8c = -15. That is not valid. You didn't use any valid mathematical operation to arrive at that equation. You don't know that c^2 - 8c = -15. The way you would get that is IF you were given c^2 - 8c +15 = 0, in which case it is a valid operation to subtract 15 from both sides of the = sign to get c^2 - 8c = -15. Edit: If the problem specifically asked you to factor by completing the square you can do the following: You can say y = x^2 - 6x + 8 y - 8 = x^2 - 6x y - 8 + 9 = x^2 - 6x + 9 y + 1 = (x - 3)^2 y = (x - 3)^2 - 1 If you weren't specifically told to complete the square then factoring the expression as (x - 4)(x - 2) works.
👍 50 | 👎 -6

Salah
a million. be conscious that ninety one factors to 13*7 be conscious that one hundred thirty five factors to 5*3*3*3 No trouble-free factors (15x-13)(9x-7) x = 13/15, 7/9 2. be conscious that each and each words is divisible by utilising 6 6x^2 - 42x + seventy two = 6(x^2 - 7x + 12) = 6(x-3)(x-4) x = 3, 4 3. to end the sq., what's a million/2 of -3 squared? a million.5 squared = 2.25 upload that to the two sides of the equation x^2 - 3x + 2.25 = 2.25 (x - a million.5) = sqrt(2.25) x - a million.5 = +/- a million.5 x = 0, 3
👍 50 | 👎 -13

Murgatroyd
you have factorised the equation correctly, but when it says complete the square, you need to look for a different of 2 squares which i can't see here sorry
👍 50 | 👎 -20

Originally Answered: Solving an equation by completing the square?
note: completing the square => x^2 + bx = c => x^2 + bx + (b/2)^2 = c + (b/2)^2 d^2 + 3d - 10 = 0 d^2 +3d = 10 d^2 + 3d + (3/2)^2 = 10 + (3/2)^2 (d + 3/2)^2 = 10 + 9/4 (d + 3/2)^2 = 49/4 . . . .taking square root of both sides d + 3/2 = ±7/2 d = 7/2 - 3/2 . . . .d = 4/2 or 2 d = -7/2 - 3/2 . . .d = -10/2 or -5 answers: { -5, 2 }

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