# Calculate: (3x+2)^2=25

## Expression: ${\left( 3x+2 \right)}^{2}=25$

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

${\left( 3x+2 \right)}^{2}-25=0$

Use ${\left( a+b \right)}^{2}={a}^{2}+2ab+{b}^{2}$ to expand the expression

$9{x}^{2}+12x+4-25=0$

Calculate the difference

$9{x}^{2}+12x-21=0$

Divide both sides of the equation by $3$

$3{x}^{2}+4x-7=0$

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

$\begin{array} { l }a=3,& b=4,& c=-7\end{array}$

Substitute $a=3$, $b=4$ and $c=-7$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -4\pm\sqrt{ {4}^{2}-4 \times 3 \times \left( -7 \right) } }{ 2 \times 3 }$

Evaluate the power

$x=\frac{ -4\pm\sqrt{ 16-4 \times 3 \times \left( -7 \right) } }{ 2 \times 3 }$

Calculate the product

$x=\frac{ -4\pm\sqrt{ 16+84 } }{ 2 \times 3 }$

Multiply the numbers

$x=\frac{ -4\pm\sqrt{ 16+84 } }{ 6 }$

$x=\frac{ -4\pm\sqrt{ 100 } }{ 6 }$

Evaluate the square root

$x=\frac{ -4\pm10 }{ 6 }$

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

$\begin{array} { l }x=\frac{ -4+10 }{ 6 },\\x=\frac{ -4-10 }{ 6 }\end{array}$

Simplify the expression

$\begin{array} { l }x=1,\\x=\frac{ -4-10 }{ 6 }\end{array}$

Simplify the expression

$\begin{array} { l }x=1,\\x=-\frac{ 7 }{ 3 }\end{array}$

The equation has $2$ solutions

\begin{align*}&\begin{array} { l }x_1=-\frac{ 7 }{ 3 },& x_2=1\end{array} \\&\begin{array} { l }x_1\approx-2.33333,& x_2=1\end{array}\end{align*}

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