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anonymous
 4 years ago
Solve the quadratic equation by completing the square
x^212+7=0
anonymous
 4 years ago
Solve the quadratic equation by completing the square x^212+7=0

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phi
 4 years ago
Best ResponseYou've already chosen the best response.0if you have time, this might help http://www.khanacademy.org/math/algebra/quadtratics/v/completingthesquare2

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1Humm. Quadratic... factor? complete the square? or quadratic formula?

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1Ah ha!! instructions say "completing the square", so I guess we'll completing the square :)

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1BTW... was the problem x^212x+7=0 (original was missing the x on the 12)

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1cool. x^2 12x + 7 = 0 step 1: move the constant over x^212x= 7

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1step 2: take half the bx term \(12 \div 2 = 6\)

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1step 3: square the number in step # \(6^2 = 36\)

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1step 4: add the number from step 3 to both sides: \[x^2 + 12x + 36 = 7 + 36\]

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1\[x^2 + 12x + 7 = 0\] \[x^2 + 12x = 7\] \[x^2 + 12x + 36 = 7+36\] step 5: factor the lefthand side, and simplify the righthand side: \[(x+6)^2 = 29\] Hint  the lefthand side always factors to (x + # from step 2, including the sign, either + or )^2

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1from this point, use the square root property to finish solving for x.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is what I started with?

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1did you just FOIL (x+6)^2 and subtract 29 to zero out the equation! Yep, that is back to where you started... :)

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1"Square Root Property" means take the square root \(\sqrt{\;\;\;}\) of both sides .

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{(x+6)^2} = \pm \sqrt {29}\]

cruffo
 4 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{(x+6)^2} = \pm \sqrt {29}\] humm.. \(\sqrt{29}\) does not simplify (other than decimal approx) so I'm gonna leave it for now... \[x+6 = \pm \sqrt{29}\] subtract 6 from both sides (but not from 29, that's inside the square root) \[x = 6 \pm \sqrt{29}\] that gives us two solutions: \[x = 6 + \sqrt{29} \approx 0.615\] and \[x = 6  \sqrt{29} \approx 11.385 \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you sooo much!!!!!:D
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