Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

2=x^{2}+x-2
Combine 2x and -x to get x.
x^{2}+x-2=2
Swap sides so that all variable terms are on the left hand side.
x^{2}+x-2-2=0
Subtract 2 from both sides.
x^{2}+x-4=0
Subtract 2 from -2 to get -4.
x=\frac{-1±\sqrt{1^{2}-4\left(-4\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1±\sqrt{1-4\left(-4\right)}}{2}
Square 1.
x=\frac{-1±\sqrt{1+16}}{2}
Multiply -4 times -4.
x=\frac{-1±\sqrt{17}}{2}
Add 1 to 16.
x=\frac{\sqrt{17}-1}{2}
Now solve the equation x=\frac{-1±\sqrt{17}}{2} when ± is plus. Add -1 to \sqrt{17}.
x=\frac{-\sqrt{17}-1}{2}
Now solve the equation x=\frac{-1±\sqrt{17}}{2} when ± is minus. Subtract \sqrt{17} from -1.
x=\frac{\sqrt{17}-1}{2} x=\frac{-\sqrt{17}-1}{2}
The equation is now solved.
2=x^{2}+x-2
Combine 2x and -x to get x.
x^{2}+x-2=2
Swap sides so that all variable terms are on the left hand side.
x^{2}+x=2+2
Add 2 to both sides.
x^{2}+x=4
Add 2 and 2 to get 4.
x^{2}+x+\left(\frac{1}{2}\right)^{2}=4+\left(\frac{1}{2}\right)^{2}
Divide 1, the coefficient of the x term, by 2 to get \frac{1}{2}. Then add the square of \frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+x+\frac{1}{4}=4+\frac{1}{4}
Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}+x+\frac{1}{4}=\frac{17}{4}
Add 4 to \frac{1}{4}.
\left(x+\frac{1}{2}\right)^{2}=\frac{17}{4}
Factor x^{2}+x+\frac{1}{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{1}{2}\right)^{2}}=\sqrt{\frac{17}{4}}
Take the square root of both sides of the equation.
x+\frac{1}{2}=\frac{\sqrt{17}}{2} x+\frac{1}{2}=-\frac{\sqrt{17}}{2}
Simplify.
x=\frac{\sqrt{17}-1}{2} x=\frac{-\sqrt{17}-1}{2}
Subtract \frac{1}{2} from both sides of the equation.