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Type a math problem

Solve for K

K=\frac{25T_{2}}{29},m\neq 0

$K=2925T_{2} ,m =0$

Steps for Solving Linear Equation

T _ { 2 } = \frac { 1.520 mm \times 290 ^ { \circ } K } { 380 mm }

$T_{2}=380mm1.520mm×290_{∘}K $

Multiply both sides of the equation by 380m^{2}.

Multiply both sides of the equation by $380m_{2}$.

T_{2}\times 380m^{2}=1.52mm\times 290K

$T_{2}×380m_{2}=1.52mm×290K$

Multiply m and m to get m^{2}.

Multiply $m$ and $m$ to get $m_{2}$.

T_{2}\times 380m^{2}=1.52m^{2}\times 290K

$T_{2}×380m_{2}=1.52m_{2}×290K$

Multiply 1.52 and 290 to get 440.8.

Multiply $1.52$ and $290$ to get $440.8$.

T_{2}\times 380m^{2}=440.8m^{2}K

$T_{2}×380m_{2}=440.8m_{2}K$

Swap sides so that all variable terms are on the left hand side.

Swap sides so that all variable terms are on the left hand side.

440.8m^{2}K=T_{2}\times 380m^{2}

$440.8m_{2}K=T_{2}×380m_{2}$

The equation is in standard form.

The equation is in standard form.

\frac{2204m^{2}}{5}K=380T_{2}m^{2}

$52204m_{2} K=380T_{2}m_{2}$

Divide both sides by 440.8m^{2}.

Divide both sides by $440.8m_{2}$.

\frac{5\times \left(\frac{2204m^{2}}{5}\right)K}{2204m^{2}}=\frac{5\times 380T_{2}m^{2}}{2204m^{2}}

$2204m_{2}5×(52204m_{2} )K =2204m_{2}5×380T_{2}m_{2} $

Dividing by 440.8m^{2} undoes the multiplication by 440.8m^{2}.

Dividing by $440.8m_{2}$ undoes the multiplication by $440.8m_{2}$.

K=\frac{5\times 380T_{2}m^{2}}{2204m^{2}}

$K=2204m_{2}5×380T_{2}m_{2} $

Divide 380T_{2}m^{2} by 440.8m^{2}.

Divide $380T_{2}m_{2}$ by $440.8m_{2}$.

K=\frac{25T_{2}}{29}

$K=2925T_{2} $

Solve for T_2

T_{2}=\frac{29K}{25},m\neq 0

$T_{2}=2529K ,m =0$

Solution Steps

T _ { 2 } = \frac { 1.520 mm \times 290 ^ { \circ } K } { 380 mm }

$T_{2}=380mm1.520mm×290_{∘}K $

Multiply m and m to get m^{2}.

Multiply $m$ and $m$ to get $m_{2}$.

T_{2}=\frac{1.52m^{2}\times 290K}{380mm}

$T_{2}=380mm1.52m_{2}×290K $

Multiply m and m to get m^{2}.

Multiply $m$ and $m$ to get $m_{2}$.

T_{2}=\frac{1.52m^{2}\times 290K}{380m^{2}}

$T_{2}=380m_{2}1.52m_{2}×290K $

Cancel out 10m^{2} in both numerator and denominator.

Cancel out $10m_{2}$ in both numerator and denominator.

T_{2}=\frac{1.52\times 29K}{38}

$T_{2}=381.52×29K $

Multiply 1.52 and 29 to get 44.08.

Multiply $1.52$ and $29$ to get $44.08$.

T_{2}=\frac{44.08K}{38}

$T_{2}=3844.08K $

Divide 44.08K by 38 to get 1.16K.

Divide $44.08K$ by $38$ to get $1.16K$.

T_{2}=1.16K

$T_{2}=1.16K$

Solve for m

m\neq 0,T_{2}=\frac{29K}{25}

$m =0,T_{2}=2529K $

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

T _ { 2 } = \frac { 1.520 mm \times 290 ^ { \circ } K } { 380 mm }

$T_{2}=380mm1.520mm×290_{∘}K $

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 380m^{2}.

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}=1.52mm\times 290K

$T_{2}×380m_{2}=1.52mm×290K$

Multiply m and m to get m^{2}.

Multiply $m$ and $m$ to get $m_{2}$.

T_{2}\times 380m^{2}=1.52m^{2}\times 290K

$T_{2}×380m_{2}=1.52m_{2}×290K$

Multiply 1.52 and 290 to get 440.8.

Multiply $1.52$ and $290$ to get $440.8$.

T_{2}\times 380m^{2}=440.8m^{2}K

$T_{2}×380m_{2}=440.8m_{2}K$

Subtract 440.8m^{2}K from both sides.

Subtract $440.8m_{2}K$ from both sides.

T_{2}\times 380m^{2}-440.8m^{2}K=0

$T_{2}×380m_{2}−440.8m_{2}K=0$

Combine all terms containing m.

Combine all terms containing $m$.

\left(T_{2}\times 380-440.8K\right)m^{2}=0

$(T_{2}×380−440.8K)m_{2}=0$

Divide both sides by 380T_{2}-440.8K.

Divide both sides by $380T_{2}−440.8K$.

\frac{\left(-\frac{2204K}{5}+380T_{2}\right)m^{2}}{-\frac{2204K}{5}+380T_{2}}=\frac{0}{-\frac{2204K}{5}+380T_{2}}

$−52204K +380T_{2}(−52204K +380T_{2})m_{2} =−52204K +380T_{2}0 $

Dividing by 380T_{2}-440.8K undoes the multiplication by 380T_{2}-440.8K.

Dividing by $380T_{2}−440.8K$ undoes the multiplication by $380T_{2}−440.8K$.

m^{2}=\frac{0}{-\frac{2204K}{5}+380T_{2}}

$m_{2}=−52204K +380T_{2}0 $

Divide 0 by 380T_{2}-440.8K.

Divide $0$ by $380T_{2}−440.8K$.

m^{2}=0

$m_{2}=0$

Take the square root of both sides of the equation.

Take the square root of both sides of the equation.

m=0 m=0

$m=0$ $m=0$

The equation is now solved. Solutions are the same.

The equation is now solved. Solutions are the same.

m=0

$m=0$

Variable m cannot be equal to 0.

Variable $m$ cannot be equal to $0$.

m\in \emptyset

$m∈∅$

Assign T_2

T_{2}≔\frac{29K}{25}

$T_{2}:=2529K $

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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.

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