Solve for x
x=10
x=0
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x^{2}+20-10x=20
Subtract 10x from both sides.
x^{2}+20-10x-20=0
Subtract 20 from both sides.
x^{2}-10x=0
Subtract 20 from 20 to get 0.
x\left(x-10\right)=0
Factor out x.
x=0 x=10
To find equation solutions, solve x=0 and x-10=0.
x^{2}+20-10x=20
Subtract 10x from both sides.
x^{2}+20-10x-20=0
Subtract 20 from both sides.
x^{2}-10x=0
Subtract 20 from 20 to get 0.
x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-10\right)±10}{2}
Take the square root of \left(-10\right)^{2}.
x=\frac{10±10}{2}
The opposite of -10 is 10.
x=\frac{20}{2}
Now solve the equation x=\frac{10±10}{2} when ± is plus. Add 10 to 10.
x=10
Divide 20 by 2.
x=\frac{0}{2}
Now solve the equation x=\frac{10±10}{2} when ± is minus. Subtract 10 from 10.
x=0
Divide 0 by 2.
x=10 x=0
The equation is now solved.
x^{2}+20-10x=20
Subtract 10x from both sides.
x^{2}+20-10x-20=0
Subtract 20 from both sides.
x^{2}-10x=0
Subtract 20 from 20 to get 0.
x^{2}-10x+\left(-5\right)^{2}=\left(-5\right)^{2}
Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-10x+25=25
Square -5.
\left(x-5\right)^{2}=25
Factor x^{2}-10x+25. 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-5\right)^{2}}=\sqrt{25}
Take the square root of both sides of the equation.
x-5=5 x-5=-5
Simplify.
x=10 x=0
Add 5 to both sides of the equation.
Examples
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{ 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}