Solve for x
x=4
x=0
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-\left(x-3\right)^{2}+\left(x-1\right)\left(1-x\right)+10=0
Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1-x^{2},1+x,x^{2}-1.
-\left(x^{2}-6x+9\right)+\left(x-1\right)\left(1-x\right)+10=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
-x^{2}+6x-9+\left(x-1\right)\left(1-x\right)+10=0
To find the opposite of x^{2}-6x+9, find the opposite of each term.
-x^{2}+6x-9+2x-x^{2}-1+10=0
Use the distributive property to multiply x-1 by 1-x and combine like terms.
-x^{2}+8x-9-x^{2}-1+10=0
Combine 6x and 2x to get 8x.
-2x^{2}+8x-9-1+10=0
Combine -x^{2} and -x^{2} to get -2x^{2}.
-2x^{2}+8x-10+10=0
Subtract 1 from -9 to get -10.
-2x^{2}+8x=0
Add -10 and 10 to get 0.
x\left(-2x+8\right)=0
Factor out x.
x=0 x=4
To find equation solutions, solve x=0 and -2x+8=0.
-\left(x-3\right)^{2}+\left(x-1\right)\left(1-x\right)+10=0
Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1-x^{2},1+x,x^{2}-1.
-\left(x^{2}-6x+9\right)+\left(x-1\right)\left(1-x\right)+10=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
-x^{2}+6x-9+\left(x-1\right)\left(1-x\right)+10=0
To find the opposite of x^{2}-6x+9, find the opposite of each term.
-x^{2}+6x-9+2x-x^{2}-1+10=0
Use the distributive property to multiply x-1 by 1-x and combine like terms.
-x^{2}+8x-9-x^{2}-1+10=0
Combine 6x and 2x to get 8x.
-2x^{2}+8x-9-1+10=0
Combine -x^{2} and -x^{2} to get -2x^{2}.
-2x^{2}+8x-10+10=0
Subtract 1 from -9 to get -10.
-2x^{2}+8x=0
Add -10 and 10 to get 0.
x=\frac{-8±\sqrt{8^{2}}}{2\left(-2\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-8±8}{2\left(-2\right)}
Take the square root of 8^{2}.
x=\frac{-8±8}{-4}
Multiply 2 times -2.
x=\frac{0}{-4}
Now solve the equation x=\frac{-8±8}{-4} when ± is plus. Add -8 to 8.
x=0
Divide 0 by -4.
x=-\frac{16}{-4}
Now solve the equation x=\frac{-8±8}{-4} when ± is minus. Subtract 8 from -8.
x=4
Divide -16 by -4.
x=0 x=4
The equation is now solved.
-\left(x-3\right)^{2}+\left(x-1\right)\left(1-x\right)+10=0
Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1-x^{2},1+x,x^{2}-1.
-\left(x^{2}-6x+9\right)+\left(x-1\right)\left(1-x\right)+10=0
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.
-x^{2}+6x-9+\left(x-1\right)\left(1-x\right)+10=0
To find the opposite of x^{2}-6x+9, find the opposite of each term.
-x^{2}+6x-9+2x-x^{2}-1+10=0
Use the distributive property to multiply x-1 by 1-x and combine like terms.
-x^{2}+8x-9-x^{2}-1+10=0
Combine 6x and 2x to get 8x.
-2x^{2}+8x-9-1+10=0
Combine -x^{2} and -x^{2} to get -2x^{2}.
-2x^{2}+8x-10+10=0
Subtract 1 from -9 to get -10.
-2x^{2}+8x=0
Add -10 and 10 to get 0.
\frac{-2x^{2}+8x}{-2}=\frac{0}{-2}
Divide both sides by -2.
x^{2}+\frac{8}{-2}x=\frac{0}{-2}
Dividing by -2 undoes the multiplication by -2.
x^{2}-4x=\frac{0}{-2}
Divide 8 by -2.
x^{2}-4x=0
Divide 0 by -2.
x^{2}-4x+\left(-2\right)^{2}=\left(-2\right)^{2}
Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-4x+4=4
Square -2.
\left(x-2\right)^{2}=4
Factor x^{2}-4x+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-2\right)^{2}}=\sqrt{4}
Take the square root of both sides of the equation.
x-2=2 x-2=-2
Simplify.
x=4 x=0
Add 2 to 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}