Solve for x
x=\frac{\sqrt{17}-3}{2}\approx 0.561552813
x=\frac{-\sqrt{17}-3}{2}\approx -3.561552813
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x^{2}-x+2\left(x-1\right)+2x=0
Use the distributive property to multiply x by x-1.
x^{2}-x+2x-2+2x=0
Use the distributive property to multiply 2 by x-1.
x^{2}+x-2+2x=0
Combine -x and 2x to get x.
x^{2}+3x-2=0
Combine x and 2x to get 3x.
x=\frac{-3±\sqrt{3^{2}-4\left(-2\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-3±\sqrt{9-4\left(-2\right)}}{2}
Square 3.
x=\frac{-3±\sqrt{9+8}}{2}
Multiply -4 times -2.
x=\frac{-3±\sqrt{17}}{2}
Add 9 to 8.
x=\frac{\sqrt{17}-3}{2}
Now solve the equation x=\frac{-3±\sqrt{17}}{2} when ± is plus. Add -3 to \sqrt{17}.
x=\frac{-\sqrt{17}-3}{2}
Now solve the equation x=\frac{-3±\sqrt{17}}{2} when ± is minus. Subtract \sqrt{17} from -3.
x=\frac{\sqrt{17}-3}{2} x=\frac{-\sqrt{17}-3}{2}
The equation is now solved.
x^{2}-x+2\left(x-1\right)+2x=0
Use the distributive property to multiply x by x-1.
x^{2}-x+2x-2+2x=0
Use the distributive property to multiply 2 by x-1.
x^{2}+x-2+2x=0
Combine -x and 2x to get x.
x^{2}+3x-2=0
Combine x and 2x to get 3x.
x^{2}+3x=2
Add 2 to both sides. Anything plus zero gives itself.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=2+\left(\frac{3}{2}\right)^{2}
Divide 3, the coefficient of the x term, by 2 to get \frac{3}{2}. Then add the square of \frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+3x+\frac{9}{4}=2+\frac{9}{4}
Square \frac{3}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}+3x+\frac{9}{4}=\frac{17}{4}
Add 2 to \frac{9}{4}.
\left(x+\frac{3}{2}\right)^{2}=\frac{17}{4}
Factor x^{2}+3x+\frac{9}{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+\frac{3}{2}\right)^{2}}=\sqrt{\frac{17}{4}}
Take the square root of both sides of the equation.
x+\frac{3}{2}=\frac{\sqrt{17}}{2} x+\frac{3}{2}=-\frac{\sqrt{17}}{2}
Simplify.
x=\frac{\sqrt{17}-3}{2} x=\frac{-\sqrt{17}-3}{2}
Subtract \frac{3}{2} from both sides of the equation.
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}