# Calculate: x-36=x^2-11x

## Expression: $x-36={x}^{2}-11x$

Move the variables to the left-hand side and change their signs

$x-36-{x}^{2}+11x=0$

Collect like terms

$12x-36-{x}^{2}=0$

Use the commutative property to reorder the terms

$-{x}^{2}+12x-36=0$

Change the signs on both sides of the equation

${x}^{2}-12x+36=0$

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

$\begin{array} { l }a=1,& b=-12,& c=36\end{array}$

Substitute $a=1$, $b=-12$ and $c=36$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 1 \times 36 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 }$

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

$x=\frac{ 12\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 }$

Evaluate the power

$x=\frac{ 12\pm\sqrt{ 144-4 \times 36 } }{ 2 }$

Multiply the numbers

$x=\frac{ 12\pm\sqrt{ 144-144 } }{ 2 }$

The sum of two opposites equals $0$

$x=\frac{ 12\pm\sqrt{ 0 } }{ 2 }$

Any root of $0$ equals $0$

$x=\frac{ 12\pm0 }{ 2 }$

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

$x=\frac{ 12 }{ 2 }$

Cancel out the common factor $2$

$x=6$

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