Solve for x
x=\frac{\sqrt{5}-3}{2}\approx -0.381966011
x=\frac{-\sqrt{5}-3}{2}\approx -2.618033989
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2\left(2x+3\right)^{2}+9-9=19-9
Subtract 9 from both sides of the equation.
2\left(2x+3\right)^{2}=19-9
Subtracting 9 from itself leaves 0.
2\left(2x+3\right)^{2}=10
Subtract 9 from 19.
\frac{2\left(2x+3\right)^{2}}{2}=\frac{10}{2}
Divide both sides by 2.
\left(2x+3\right)^{2}=\frac{10}{2}
Dividing by 2 undoes the multiplication by 2.
\left(2x+3\right)^{2}=5
Divide 10 by 2.
2x+3=\sqrt{5} 2x+3=-\sqrt{5}
Take the square root of both sides of the equation.
2x+3-3=\sqrt{5}-3 2x+3-3=-\sqrt{5}-3
Subtract 3 from both sides of the equation.
2x=\sqrt{5}-3 2x=-\sqrt{5}-3
Subtracting 3 from itself leaves 0.
2x=\sqrt{5}-3
Subtract 3 from \sqrt{5}.
2x=-\sqrt{5}-3
Subtract 3 from -\sqrt{5}.
\frac{2x}{2}=\frac{\sqrt{5}-3}{2} \frac{2x}{2}=\frac{-\sqrt{5}-3}{2}
Divide both sides by 2.
x=\frac{\sqrt{5}-3}{2} x=\frac{-\sqrt{5}-3}{2}
Dividing by 2 undoes the multiplication by 2.
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}