Type a math problem
Solve for K
Steps for Solving Linear Equation
Multiply both sides of the equation by .
Multiply and to get .
Multiply and to get .
Swap sides so that all variable terms are on the left hand side.
The equation is in standard form.
Divide both sides by .
Dividing by undoes the multiplication by .
Divide by .
Solve for T_2
Solution Steps
Multiply and to get .
Multiply and to get .
Cancel out in both numerator and denominator.
Multiply and to get .
Divide by to get .
Solve for m
Steps by Finding Square Root
Steps by Finding Square Root
Variable cannot be equal to since division by zero is not defined. Multiply both sides of the equation by .
Multiply and to get .
Multiply and to get .
Subtract from both sides.
Combine all terms containing .
Divide both sides by .
Dividing by undoes the multiplication by .
Divide by .
Take the square root of both sides of the equation.
The equation is now solved. Solutions are the same.
Variable cannot be equal to .
Assign T_2
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T_{2}\times 380m^{2}=1.52mm\times 290K
Multiply both sides of the equation by 380m^{2}.
T_{2}\times 380m^{2}=1.52m^{2}\times 290K
Multiply m and m to get m^{2}.
T_{2}\times 380m^{2}=440.8m^{2}K
Multiply 1.52 and 290 to get 440.8.
440.8m^{2}K=T_{2}\times 380m^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{2204m^{2}}{5}K=380T_{2}m^{2}
The equation is in standard form.
\frac{5\times \left(\frac{2204m^{2}}{5}\right)K}{2204m^{2}}=\frac{5\times 380T_{2}m^{2}}{2204m^{2}}
Divide both sides by 440.8m^{2}.
K=\frac{5\times 380T_{2}m^{2}}{2204m^{2}}
Dividing by 440.8m^{2} undoes the multiplication by 440.8m^{2}.
K=\frac{25T_{2}}{29}
Divide 380T_{2}m^{2} by 440.8m^{2}.
T_{2}=\frac{1.52m^{2}\times 290K}{380mm}
Multiply m and m to get m^{2}.
T_{2}=\frac{1.52m^{2}\times 290K}{380m^{2}}
Multiply m and m to get m^{2}.
T_{2}=\frac{1.52\times 29K}{38}
Cancel out 10m^{2} in both numerator and denominator.
T_{2}=\frac{44.08K}{38}
Multiply 1.52 and 29 to get 44.08.
T_{2}=1.16K
Divide 44.08K by 38 to get 1.16K.
T_{2}\times 380m^{2}=1.52mm\times 290K
Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 380m^{2}.
T_{2}\times 380m^{2}=1.52m^{2}\times 290K
Multiply m and m to get m^{2}.
T_{2}\times 380m^{2}=440.8m^{2}K
Multiply 1.52 and 290 to get 440.8.
T_{2}\times 380m^{2}-440.8m^{2}K=0
Subtract 440.8m^{2}K from both sides.
\left(T_{2}\times 380-440.8K\right)m^{2}=0
Combine all terms containing m.
\frac{\left(-\frac{2204K}{5}+380T_{2}\right)m^{2}}{-\frac{2204K}{5}+380T_{2}}=\frac{0}{-\frac{2204K}{5}+380T_{2}}
Divide both sides by 380T_{2}-440.8K.
m^{2}=\frac{0}{-\frac{2204K}{5}+380T_{2}}
Dividing by 380T_{2}-440.8K undoes the multiplication by 380T_{2}-440.8K.
m^{2}=0
Divide 0 by 380T_{2}-440.8K.
m=0 m=0
Take the square root of both sides of the equation.
m=0
The equation is now solved. Solutions are the same.
m\in \emptyset
Variable m cannot be equal to 0.
T_{2}\times 380m^{2}=1.52mm\times 290K
Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 380m^{2}.
T_{2}\times 380m^{2}=1.52m^{2}\times 290K
Multiply m and m to get m^{2}.
T_{2}\times 380m^{2}=440.8m^{2}K
Multiply 1.52 and 290 to get 440.8.
T_{2}\times 380m^{2}-440.8m^{2}K=0
Subtract 440.8m^{2}K from both sides.
\left(T_{2}\times 380-440.8K\right)m^{2}=0
Combine all terms containing m.
\left(-\frac{2204K}{5}+380T_{2}\right)m^{2}=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
m=\frac{0±\sqrt{0^{2}}}{2\left(-\frac{2204K}{5}+380T_{2}\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 380T_{2}-440.8K for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
m=\frac{0±0}{2\left(-\frac{2204K}{5}+380T_{2}\right)}
Take the square root of 0^{2}=0.
m=\frac{0}{-\frac{4408K}{5}+760T_{2}}
Multiply 2 times 380T_{2}-440.8K.
m=0
Divide 0 by 760T_{2}-\frac{4408K}{5}.
m\in \emptyset
Variable m cannot be equal to 0.