Solve for: m^2-5m-14=0

Expression: ${m}^{2}-5m-14=0$

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

$\begin{array} { l }a=1,& b=-5,& c=-14\end{array}$

Substitute $a=1$, $b=-5$ and $c=-14$ into the quadratic formula $m=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$m=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 1 \times \left( -14 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$m=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times \left( -14 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$m=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times \left( -14 \right) } }{ 2 }$

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

$m=\frac{ 5\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times \left( -14 \right) } }{ 2 }$

Evaluate the power

$m=\frac{ 5\pm\sqrt{ 25-4 \times \left( -14 \right) } }{ 2 }$

Multiply the numbers

$m=\frac{ 5\pm\sqrt{ 25+56 } }{ 2 }$

Add the numbers

$m=\frac{ 5\pm\sqrt{ 81 } }{ 2 }$

Evaluate the square root

$m=\frac{ 5\pm9 }{ 2 }$

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

$\begin{array} { l }m=\frac{ 5+9 }{ 2 },\\m=\frac{ 5-9 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }m=7,\\m=\frac{ 5-9 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }m=7,\\m=-2\end{array}$

The equation has $2$ solutions

$\begin{array} { l }m_1=-2,& m_2=7\end{array}$