Solve for x
x=10\sqrt{5}\approx 22.360679775
x=-10\sqrt{5}\approx -22.360679775
Graph
Share
Copied to clipboard
x^{2}=500
Multiply 20 and 25 to get 500.
x=10\sqrt{5} x=-10\sqrt{5}
Take the square root of both sides of the equation.
x^{2}=500
Multiply 20 and 25 to get 500.
x^{2}-500=0
Subtract 500 from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(-500\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-500\right)}}{2}
Square 0.
x=\frac{0±\sqrt{2000}}{2}
Multiply -4 times -500.
x=\frac{0±20\sqrt{5}}{2}
Take the square root of 2000.
x=10\sqrt{5}
Now solve the equation x=\frac{0±20\sqrt{5}}{2} when ± is plus.
x=-10\sqrt{5}
Now solve the equation x=\frac{0±20\sqrt{5}}{2} when ± is minus.
x=10\sqrt{5} x=-10\sqrt{5}
The equation is now solved.
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}