Evaluate: m^2-8m+12=0

Expression: ${m}^{2}-8m+12=0$

Identify the coefficients $a$, $b$ and $c$ of the quadratic equation

$\begin{array} { l }a=1,& b=-8,& c=12\end{array}$

Substitute $a=1$, $b=-8$ and $c=12$ into the quadratic formula $m=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$m=\frac{ -\left( -8 \right)\pm\sqrt{ {\left( -8 \right)}^{2}-4 \times 1 \times 12 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$m=\frac{ -\left( -8 \right)\pm\sqrt{ {\left( -8 \right)}^{2}-4 \times 12 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$m=\frac{ -\left( -8 \right)\pm\sqrt{ {\left( -8 \right)}^{2}-4 \times 12 } }{ 2 }$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$m=\frac{ 8\pm\sqrt{ {\left( -8 \right)}^{2}-4 \times 12 } }{ 2 }$

Evaluate the power

$m=\frac{ 8\pm\sqrt{ 64-4 \times 12 } }{ 2 }$

Multiply the numbers

$m=\frac{ 8\pm\sqrt{ 64-48 } }{ 2 }$

Subtract the numbers

$m=\frac{ 8\pm\sqrt{ 16 } }{ 2 }$

Evaluate the square root

$m=\frac{ 8\pm4 }{ 2 }$

Write the solutions, one with a $+$ sign and one with a $-$ sign

$\begin{array} { l }m=\frac{ 8+4 }{ 2 },\\m=\frac{ 8-4 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }m=6,\\m=\frac{ 8-4 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }m=6,\\m=2\end{array}$

The equation has $2$ solutions

$\begin{array} { l }m_1=2,& m_2=6\end{array}$