Completing the square is done by taking the coefficient of xx, halving it and then squaring it. Then we add the new value to both sides of the equation.
Take the coefficient of the middle term, divide it by two and then square it.
x2x2-12−12xx
==
-22−22
Coefficient of the middle term
-12−12÷2÷2
==
-6−6
Divide it by 22
(-6)2(−6)2
==
3636
Square
This number will make the left side a perfect square.
Add 3636 to both sides of the equation to keep the balance.
x2-12xx2−12x
==
-22−22
x2-12xx2−12x+36+36
==
-22−22+36+36
Add 3636 to both sides
x2-12x+36x2−12x+36
==
1414
Now, transform the left side into a square of a binomial by factoring or using cross method.
(x-6)(x-6)(x−6)(x−6)
==
1414
(x-6)2(x−6)2
==
1414
Finally, take the square root of both sides and continue solving for xx.
(x-6)2(x−6)2
==
1414
√(x-6)2√(x−6)2
==
√14√14
Take the square root
x-6x−6
==
±√14±√14
Square rooting a number gives a plus and minus solution
Completing the square is done by taking the coefficient of xx, halving it and then squaring it. Then we add the new value to both sides of the equation.
Take the coefficient of the middle term, divide it by two and then square it.
x2+x2+66x+13x+13
==
00
Coefficient of the middle term
66÷2÷2
==
33
Divide it by 22
(3)2(3)2
==
99
Square
This number will make a perfect square on the left side.
Add and subtract 99 to the left side of the equation to keep the balance, then form a square of a binomial
x2+6x+13x2+6x+13
==
00
x2+6xx2+6x+9-9+9−9+13+13
==
00
(x+3)2-9+13(x+3)2−9+13
==
00
(x+3)2+4(x+3)2+4
==
00
Move the constant to the right
(x+3)2+4(x+3)2+4
==
00
(x+3)2+4(x+3)2+4-4−4
==
00-4−4
Subtract 44 from both sides
(x+3)2(x+3)2
==
-4−4
Finally, take the square root of both sides and continue solving for xx.
(x+3)2(x+3)2
==
-4−4
√(x+3)2√(x+3)2
==
√-4√−4
Remember that a negative value inside a surd will give out imaginary roots. Therefore, this equation has no real roots
Completing the square is done by taking the coefficient of xx, halving it and then squaring it. Then we add the new value to both sides of the equation.
Take the coefficient of the middle term, divide it by two and then square it.
x2+x2+33x-6x−6
==
00
Coefficient of the middle term
33÷2÷2
==
3232
Divide it by 22
(32)2(32)2
==
9494
Square
This number will make a perfect square on the left side.
Add and subtract 9494 to the left side of the equation to keep the balance, then form a square of a binomial
x2+3x-6x2+3x−6
==
00
x2+3xx2+3x+94-94+94−94-6−6
==
00
(x+32)2-94-6(x+32)2−94−6
==
00
(x+32)2-334(x+32)2−334
==
00
Move the constant to the right
(x+32)2-334(x+32)2−334
=
0
(x+32)2-334+334
=
0+334
Add 334 to both sides
(x+32)2
=
334
Finally, take the square root of both sides and continue solving for x.
Completing the square is done by taking the coefficient of x, halving it and then squaring it. Then we add the new value to both sides of the equation.
Move k terms to the left
k2-4k
=
2k+18
k2-4k-2k
=
2k+18-2k
Subtract 2k from both sides
k2-6k
=
18
Take the coefficient of the middle term, divide it by two and then square it.
k2-6k
=
18
Coefficient of the middle term
-6÷2
=
-3
Divide it by 2
(-3)2
=
9
Square
This number will make a perfect square on the left side.
Add 9 to both sides of the equation to keep the balance, then form a square of a binomial
k2-6k
=
18
k2-6k+9
=
18+9
(x-3)2
=
27
Finally, take the square root of both sides and continue solving for x.
Completing the square is done by taking the coefficient of x, halving it and then squaring it. Then we add the new value to both sides of the equation.
Take the coefficient of the middle term, divide it by two and then square it.
u2+1.8u-2.2
=
0
Coefficient of the middle term
1.8÷2
=
0.9
Divide it by 2
(0.9)2
=
0.81
Square
This number will make a perfect square on the left side.
Add and subtract 0.81 to the left side of the equation to keep the balance, then form a square of a binomial
u2+1.8u-2.2
=
0
u2+1.8u+0.81-0.81-2.2
=
0
(u+0.9)2-0.81-2.2
=
0
(u+0.9)2-3.01
=
0
Move the constant to the right
(u+0.9)2-3.01
=
0
(u+0.9)2-3.01+3.01
=
0+3.01
Add 3.01 to both sides
(u+0.9)2
=
3.01
Finally, take the square root of both sides and continue solving for x.