Solve for m
m=\sqrt{3}+2\approx 3.732050808
m=2-\sqrt{3}\approx 0.267949192
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mm+1=4m
Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m.
m^{2}+1=4m
Multiply m and m to get m^{2}.
m^{2}+1-4m=0
Subtract 4m from both sides.
m^{2}-4m+1=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
m=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
m=\frac{-\left(-4\right)±\sqrt{16-4}}{2}
Square -4.
m=\frac{-\left(-4\right)±\sqrt{12}}{2}
Add 16 to -4.
m=\frac{-\left(-4\right)±2\sqrt{3}}{2}
Take the square root of 12.
m=\frac{4±2\sqrt{3}}{2}
The opposite of -4 is 4.
m=\frac{2\sqrt{3}+4}{2}
Now solve the equation m=\frac{4±2\sqrt{3}}{2} when ± is plus. Add 4 to 2\sqrt{3}.
m=\sqrt{3}+2
Divide 4+2\sqrt{3} by 2.
m=\frac{4-2\sqrt{3}}{2}
Now solve the equation m=\frac{4±2\sqrt{3}}{2} when ± is minus. Subtract 2\sqrt{3} from 4.
m=2-\sqrt{3}
Divide 4-2\sqrt{3} by 2.
m=\sqrt{3}+2 m=2-\sqrt{3}
The equation is now solved.
mm+1=4m
Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m.
m^{2}+1=4m
Multiply m and m to get m^{2}.
m^{2}+1-4m=0
Subtract 4m from both sides.
m^{2}-4m=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
m^{2}-4m+\left(-2\right)^{2}=-1+\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.
m^{2}-4m+4=-1+4
Square -2.
m^{2}-4m+4=3
Add -1 to 4.
\left(m-2\right)^{2}=3
Factor m^{2}-4m+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(m-2\right)^{2}}=\sqrt{3}
Take the square root of both sides of the equation.
m-2=\sqrt{3} m-2=-\sqrt{3}
Simplify.
m=\sqrt{3}+2 m=2-\sqrt{3}
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}