# Calculate: x^2-14=-5

## Expression: ${x}^{2}-14=-5$

Move the constant to the left-hand side and change its sign

${x}^{2}-14+5=0$

Calculate the sum

${x}^{2}-9=0$

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

$\begin{array} { l }a=1,& b=0,& c=-9\end{array}$

Substitute $a=1$, $b=0$ and $c=-9$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -0\pm\sqrt{ {0}^{2}-4 \times 1 \times \left( -9 \right) } }{ 2 \times 1 }$

Removing $0$ doesn't change the value, so remove it from the expression

$x=\frac{ \sqrt{ {0}^{2}-4 \times 1 \times \left( -9 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ \sqrt{ {0}^{2}-4 \times \left( -9 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ \sqrt{ {0}^{2}-4 \times \left( -9 \right) } }{ 2 }$

$0$ raised to any positive power equals $0$

$x=\frac{ \sqrt{ 0-4 \times \left( -9 \right) } }{ 2 }$

Multiply the numbers

$x=\frac{ \sqrt{ 0+36 } }{ 2 }$

Removing $0$ doesn't change the value, so remove it from the expression

$x=\frac{ \sqrt{ 36 } }{ 2 }$

Evaluate the square root

$x=\frac{ 6 }{ 2 }$

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

$\begin{array} { l }x=\frac{ 6 }{ 2 },\\x=\frac{ -6 }{ 2 }\end{array}$

Cancel out the common factor $2$

$\begin{array} { l }x=3,\\x=\frac{ -6 }{ 2 }\end{array}$

Cancel out the common factor $2$

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

The equation has $2$ solutions

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

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