Solve for x
x=-\frac{2}{9}\approx -0.222222222
x=0
Graph
Share
Copied to clipboard
x\left(9x+2\right)=0
Factor out x.
x=0 x=-\frac{2}{9}
To find equation solutions, solve x=0 and 9x+2=0.
9x^{2}+2x=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-2±\sqrt{2^{2}}}{2\times 9}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±2}{2\times 9}
Take the square root of 2^{2}.
x=\frac{-2±2}{18}
Multiply 2 times 9.
x=\frac{0}{18}
Now solve the equation x=\frac{-2±2}{18} when ± is plus. Add -2 to 2.
x=0
Divide 0 by 18.
x=-\frac{4}{18}
Now solve the equation x=\frac{-2±2}{18} when ± is minus. Subtract 2 from -2.
x=-\frac{2}{9}
Reduce the fraction \frac{-4}{18} to lowest terms by extracting and canceling out 2.
x=0 x=-\frac{2}{9}
The equation is now solved.
9x^{2}+2x=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
\frac{9x^{2}+2x}{9}=\frac{0}{9}
Divide both sides by 9.
x^{2}+\frac{2}{9}x=\frac{0}{9}
Dividing by 9 undoes the multiplication by 9.
x^{2}+\frac{2}{9}x=0
Divide 0 by 9.
x^{2}+\frac{2}{9}x+\left(\frac{1}{9}\right)^{2}=\left(\frac{1}{9}\right)^{2}
Divide \frac{2}{9}, the coefficient of the x term, by 2 to get \frac{1}{9}. Then add the square of \frac{1}{9} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{2}{9}x+\frac{1}{81}=\frac{1}{81}
Square \frac{1}{9} by squaring both the numerator and the denominator of the fraction.
\left(x+\frac{1}{9}\right)^{2}=\frac{1}{81}
Factor x^{2}+\frac{2}{9}x+\frac{1}{81}. 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}{9}\right)^{2}}=\sqrt{\frac{1}{81}}
Take the square root of both sides of the equation.
x+\frac{1}{9}=\frac{1}{9} x+\frac{1}{9}=-\frac{1}{9}
Simplify.
x=0 x=-\frac{2}{9}
Subtract \frac{1}{9} 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}