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\left(x-4\right)x+4=0
Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.
x^{2}-4x+4=0
Use the distributive property to multiply x-4 by x.
a+b=-4 ab=4
To solve the equation, factor x^{2}-4x+4 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.
-1,-4 -2,-2
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 4.
-1-4=-5 -2-2=-4
Calculate the sum for each pair.
a=-2 b=-2
The solution is the pair that gives sum -4.
\left(x-2\right)\left(x-2\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
\left(x-2\right)^{2}
Rewrite as a binomial square.
x=2
To find equation solution, solve x-2=0.
\left(x-4\right)x+4=0
Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.
x^{2}-4x+4=0
Use the distributive property to multiply x-4 by x.
a+b=-4 ab=1\times 4=4
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx+4. To find a and b, set up a system to be solved.
-1,-4 -2,-2
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 4.
-1-4=-5 -2-2=-4
Calculate the sum for each pair.
a=-2 b=-2
The solution is the pair that gives sum -4.
\left(x^{2}-2x\right)+\left(-2x+4\right)
Rewrite x^{2}-4x+4 as \left(x^{2}-2x\right)+\left(-2x+4\right).
x\left(x-2\right)-2\left(x-2\right)
Factor out x in the first and -2 in the second group.
\left(x-2\right)\left(x-2\right)
Factor out common term x-2 by using distributive property.
\left(x-2\right)^{2}
Rewrite as a binomial square.
x=2
To find equation solution, solve x-2=0.
\left(x-4\right)x+4=0
Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.
x^{2}-4x+4=0
Use the distributive property to multiply x-4 by x.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 4}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-4\right)±\sqrt{16-4\times 4}}{2}
Square -4.
x=\frac{-\left(-4\right)±\sqrt{16-16}}{2}
Multiply -4 times 4.
x=\frac{-\left(-4\right)±\sqrt{0}}{2}
Add 16 to -16.
x=-\frac{-4}{2}
Take the square root of 0.
x=\frac{4}{2}
The opposite of -4 is 4.
x=2
Divide 4 by 2.
\left(x-4\right)x+4=0
Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.
x^{2}-4x+4=0
Use the distributive property to multiply x-4 by x.
\left(x-2\right)^{2}=0
Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-2\right)^{2}}=\sqrt{0}
Take the square root of both sides of the equation.
x-2=0 x-2=0
Simplify.
x=2 x=2
Add 2 to both sides of the equation.
x=2
The equation is now solved. Solutions are the same.