# Calculate: x^2-200=0

## Expression: ${x}^{2}-200=0$

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

$\begin{array} { l }a=1,& b=0,& c=-200\end{array}$

Substitute $a=1$, $b=0$ and $c=-200$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -0\pm\sqrt{ {0}^{2}-4 \times 1 \times \left( -200 \right) } }{ 2 \times 1 }$

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

$x=\frac{ \sqrt{ {0}^{2}-4 \times 1 \times \left( -200 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ \sqrt{ {0}^{2}-4 \times \left( -200 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ \sqrt{ {0}^{2}-4 \times \left( -200 \right) } }{ 2 }$

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

$x=\frac{ \sqrt{ 0-4 \times \left( -200 \right) } }{ 2 }$

Multiply the numbers

$x=\frac{ \sqrt{ 0+800 } }{ 2 }$

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

$x=\frac{ \sqrt{ 800 } }{ 2 }$

$x=\frac{ 20\sqrt{ 2 } }{ 2 }$

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

$\begin{array} { l }x=\frac{ 20\sqrt{ 2 } }{ 2 },\\x=\frac{ -20\sqrt{ 2 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=10\sqrt{ 2 },\\x=\frac{ -20\sqrt{ 2 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=10\sqrt{ 2 },\\x=-10\sqrt{ 2 }\end{array}$

The equation has $2$ solutions

\begin{align*}&\begin{array} { l }x_1=-10\sqrt{ 2 },& x_2=10\sqrt{ 2 }\end{array} \\&\begin{array} { l }x_1\approx-14.14214,& x_2\approx14.14214\end{array}\end{align*}

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