# Calculate: x^2+3x-18=0

## Expression: ${x}^{2}+3x-18=0$

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

$\begin{array} { l }a=1,& b=3,& c=-18\end{array}$

Substitute $a=1$, $b=3$ and $c=-18$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -3\pm\sqrt{ {3}^{2}-4 \times 1 \times \left( -18 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -3\pm\sqrt{ {3}^{2}-4 \times \left( -18 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -3\pm\sqrt{ {3}^{2}-4 \times \left( -18 \right) } }{ 2 }$

Evaluate the power

$x=\frac{ -3\pm\sqrt{ 9-4 \times \left( -18 \right) } }{ 2 }$

Multiply the numbers

$x=\frac{ -3\pm\sqrt{ 9+72 } }{ 2 }$

$x=\frac{ -3\pm\sqrt{ 81 } }{ 2 }$

Evaluate the square root

$x=\frac{ -3\pm9 }{ 2 }$

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

$\begin{array} { l }x=\frac{ -3+9 }{ 2 },\\x=\frac{ -3-9 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=3,\\x=\frac{ -3-9 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=3,\\x=-6\end{array}$

The equation has $2$ solutions

$\begin{array} { l }x_1=-6,& x_2=3\end{array}$

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