Completing the square?

Question

The question is to solve for X by completing the square:

x^2 - 30 = 8x

Serious answers only, please and thank you.

Answer 1

x^2-30=8x
x^2-8x-30=0
x^2-8x+16-30-16=0
(x-4)^2-46=0
To get the constant term(in this case 16) needed to complete the square, take half the coefficient of the x term and then square it. CAUTION! Make sure the coefficient of the x^2 term is +1 before you do this.

Answer 2

x² - 30 = 8x
==> x² - 8x = 30
==> x² - 8x + (-8/2)² = 30 + (-8/2)²
==> x² - 8x + (-4)² = 30 + (-8/2)²

Ok.....here's the part you need to pay attention to. That last equation....you see that term "(-4)² "...THAT is the term that you use....INCLUDING THE SIGN in the re-write of the 'perfect square' on the next line below. If you make note of this you will ALWAYS know what term that is to be written on the left hand side: "(x - 4)²".

See that? x - 4.....that minus sign is because the 4 is negative. So.....don't square the sign in this step. Just do the division by two and leave it at that, or you run the risk of making a sign mistake.



==> (x - 4)² = 46
==> x - 4 = ±√(46)

▪▪▪▪> x = ±√(46) + 4
(done)

Answer 3

In a quadratic equation with x^2 coefficient os 1 the square is completed by squaring half of the x coefficient and adding it to both sides of the equation which does not change the solution, only the form of the equation.

So in you equation, rearranging terms to get xs on the left and numbers on the right, we get

x^2 -8x = 30 . Now we complete the square by taking half of -8 which is -4 and squaring it to get 16 and then add 16 to both sides to get

x^2 -8x +16 = 16

Now that we have a perfect square we just take square root of x^2 and 16 to factor and get

(x-4)^2 = 16 +30 = 46 which we can solve by taking sqrt of b oth side to get

x-4 = +/- sqrt(46) so x = 4 +/- sqrt(46)

Answer 4

x^2 - 30 = 8x
x^2 - 8x = 30

Take the number in front of the x (8), cut that in half (4), then square it (16). Add that number to both sides.

x^2 - 8x + 16 = 30 + 16
x^2 - 8x + 16 = 46
(x - 4)^2 = 46
x - 4 = +- sqrt 46
x = 4 +- sqrt 46

Answer 5

x^2 - 30 = 8x
x^2 - 8x - 30 = 0
x^2- 8x + 16 - 16 - 30
(x-4)^2 - 46 = 0

Answer 6

x^2 - 8x = 30

x^2 - 8x + 16 = 30 + 16

(x - 4)^2 = 46

(x - 4) = +/- sqrt 46

x = 4 +/- sqrt 46

Answer 7

x^2 - 30 = 8x
x^2 - 8x = 30
x^2 - 8x + 16 = 30+ 16
(x-4)^2 = 36

etc

Answer 8

x^2 - 30 = 8x
x^2-8x=30
x^2-8x+(-8/2)^2=30+(-8/2)^2
x^2-8x+16=30+16
x^2-8x+16=46
(x-4)^2=46
x-4=+/-sqrt(46)
x=+/-sqrt(46)+4

Answer 9

x² - 8x = 30
x² - 8x + 16 = 46
(x - 4)² = 46
x - 4 = ±√46
x = 4 ± √46

Answer 10

x^2 - 30 = 8x

x^2-8x=30

x^2-8x+(-8/2)^2=30+(-8/2)^2

x^2-8x+16=30+16

x^2-8x+16=46

(x-4)^2=46

x-4=+/-sqrt(46)

x=+/-sqrt(46)+4
ain't me right?