Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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2x^{2}+2x+5=x\left(2x-3\right)+5\left(x+1\right)
Use the distributive property to multiply 2x by x+1.
2x^{2}+2x+5=2x^{2}-3x+5\left(x+1\right)
Use the distributive property to multiply x by 2x-3.
2x^{2}+2x+5=2x^{2}-3x+5x+5
Use the distributive property to multiply 5 by x+1.
2x^{2}+2x+5=2x^{2}+2x+5
Combine -3x and 5x to get 2x.
2x^{2}+2x+5-2x^{2}=2x+5
Subtract 2x^{2} from both sides.
2x+5=2x+5
Combine 2x^{2} and -2x^{2} to get 0.
2x+5-2x=5
Subtract 2x from both sides.
5=5
Combine 2x and -2x to get 0.
\text{true}
Compare 5 and 5.
x\in \mathrm{C}
This is true for any x.
2x^{2}+2x+5=x\left(2x-3\right)+5\left(x+1\right)
Use the distributive property to multiply 2x by x+1.
2x^{2}+2x+5=2x^{2}-3x+5\left(x+1\right)
Use the distributive property to multiply x by 2x-3.
2x^{2}+2x+5=2x^{2}-3x+5x+5
Use the distributive property to multiply 5 by x+1.
2x^{2}+2x+5=2x^{2}+2x+5
Combine -3x and 5x to get 2x.
2x^{2}+2x+5-2x^{2}=2x+5
Subtract 2x^{2} from both sides.
2x+5=2x+5
Combine 2x^{2} and -2x^{2} to get 0.
2x+5-2x=5
Subtract 2x from both sides.
5=5
Combine 2x and -2x to get 0.
\text{true}
Compare 5 and 5.
x\in \mathrm{R}
This is true for any x.
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}