Solve for x
x=1
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x^{2}-2x+1=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
a+b=-2 ab=1
To solve the equation, factor x^{2}-2x+1 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.
a=-1 b=-1
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.
\left(x-1\right)\left(x-1\right)
Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.
\left(x-1\right)^{2}
Rewrite as a binomial square.
x=1
To find equation solution, solve x-1=0.
x^{2}-2x+1=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
a+b=-2 ab=1\times 1=1
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx+1. To find a and b, set up a system to be solved.
a=-1 b=-1
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.
\left(x^{2}-x\right)+\left(-x+1\right)
Rewrite x^{2}-2x+1 as \left(x^{2}-x\right)+\left(-x+1\right).
x\left(x-1\right)-\left(x-1\right)
Factor out x in the first and -1 in the second group.
\left(x-1\right)\left(x-1\right)
Factor out common term x-1 by using distributive property.
\left(x-1\right)^{2}
Rewrite as a binomial square.
x=1
To find equation solution, solve x-1=0.
x^{2}-2x+1=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4}}{2}
Square -2.
x=\frac{-\left(-2\right)±\sqrt{0}}{2}
Add 4 to -4.
x=-\frac{-2}{2}
Take the square root of 0.
x=\frac{2}{2}
The opposite of -2 is 2.
x=1
Divide 2 by 2.
\sqrt{\left(x-1\right)^{2}}=\sqrt{0}
Take the square root of both sides of the equation.
x-1=0 x-1=0
Simplify.
x=1 x=1
Add 1 to both sides of the equation.
x=1
The equation is now solved. Solutions are the same.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}