Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

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.