Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

x^{2}-4x+2=0
Swap sides so that all variable terms are on the left hand side.
x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-4\right)±\sqrt{16-4\times 2}}{2}
Square -4.
x=\frac{-\left(-4\right)±\sqrt{16-8}}{2}
Multiply -4 times 2.
x=\frac{-\left(-4\right)±\sqrt{8}}{2}
Add 16 to -8.
x=\frac{-\left(-4\right)±2\sqrt{2}}{2}
Take the square root of 8.
x=\frac{4±2\sqrt{2}}{2}
The opposite of -4 is 4.
x=\frac{2\sqrt{2}+4}{2}
Now solve the equation x=\frac{4±2\sqrt{2}}{2} when ± is plus. Add 4 to 2\sqrt{2}.
x=\sqrt{2}+2
Divide 4+2\sqrt{2} by 2.
x=\frac{4-2\sqrt{2}}{2}
Now solve the equation x=\frac{4±2\sqrt{2}}{2} when ± is minus. Subtract 2\sqrt{2} from 4.
x=2-\sqrt{2}
Divide 4-2\sqrt{2} by 2.
x=\sqrt{2}+2 x=2-\sqrt{2}
The equation is now solved.
x^{2}-4x+2=0
Swap sides so that all variable terms are on the left hand side.
x^{2}-4x=-2
Subtract 2 from both sides. Anything subtracted from zero gives its negation.
x^{2}-4x+\left(-2\right)^{2}=-2+\left(-2\right)^{2}
Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-4x+4=-2+4
Square -2.
x^{2}-4x+4=2
Add -2 to 4.
\left(x-2\right)^{2}=2
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{2}
Take the square root of both sides of the equation.
x-2=\sqrt{2} x-2=-\sqrt{2}
Simplify.
x=\sqrt{2}+2 x=2-\sqrt{2}
Add 2 to both sides of the equation.