Calculate: 4x^2-225=0

Expression: $4{x}^{2}-225=0$

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

$\begin{array} { l }a=4,& b=0,& c=-225\end{array}$

Substitute $a=4$, $b=0$ and $c=-225$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -0\pm\sqrt{ {0}^{2}-4 \times 4 \times \left( -225 \right) } }{ 2 \times 4 }$

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

$x=\frac{ \sqrt{ {0}^{2}-4 \times 4 \times \left( -225 \right) } }{ 2 \times 4 }$

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

$x=\frac{ \sqrt{ 0-4 \times 4 \times \left( -225 \right) } }{ 2 \times 4 }$

Calculate the product

$x=\frac{ \sqrt{ 0+3600 } }{ 2 \times 4 }$

Multiply the numbers

$x=\frac{ \sqrt{ 0+3600 } }{ 8 }$

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

$x=\frac{ \sqrt{ 3600 } }{ 8 }$

Evaluate the square root

$x=\frac{ 60 }{ 8 }$

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

$\begin{array} { l }x=\frac{ 60 }{ 8 },\\x=\frac{ -60 }{ 8 }\end{array}$

Cancel out the common factor $4$

$\begin{array} { l }x=\frac{ 15 }{ 2 },\\x=\frac{ -60 }{ 8 }\end{array}$

Simplify the expression

$\begin{array} { l }x=\frac{ 15 }{ 2 },\\x=-\frac{ 15 }{ 2 }\end{array}$

The equation has $2$ solutions

$\begin{align*}&\begin{array} { l }x_1=-\frac{ 15 }{ 2 },& x_2=\frac{ 15 }{ 2 }\end{array} \\&\begin{array} { l }x_1=-7.5,& x_2=7.5\end{array}\end{align*}$