# Calculate: 2x * (x+4)=(x-3) * (x-3)

## Expression: $2x \times \left( x+4 \right)=\left( x-3 \right) \times \left( x-3 \right)$

Distribute $2x$ through the parentheses

$2{x}^{2}+8x=\left( x-3 \right) \times \left( x-3 \right)$

The factor $x-3$ repeats $2$ times, so the base is $x-3$ and the exponent is $2$

$2{x}^{2}+8x={\left( x-3 \right)}^{2}$

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

$2{x}^{2}+8x={x}^{2}-6x+9$

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

$2{x}^{2}+8x-{x}^{2}+6x-9=0$

Collect like terms

${x}^{2}+8x+6x-9=0$

Collect like terms

${x}^{2}+14x-9=0$

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

$\begin{array} { l }a=1,& b=14,& c=-9\end{array}$

Substitute $a=1$, $b=14$ and $c=-9$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times 1 \times \left( -9 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times \left( -9 \right) } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times \left( -9 \right) } }{ 2 }$

Evaluate the power

$x=\frac{ -14\pm\sqrt{ 196-4 \times \left( -9 \right) } }{ 2 }$

Multiply the numbers

$x=\frac{ -14\pm\sqrt{ 196+36 } }{ 2 }$

$x=\frac{ -14\pm\sqrt{ 232 } }{ 2 }$

$x=\frac{ -14\pm2\sqrt{ 58 } }{ 2 }$

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

$\begin{array} { l }x=\frac{ -14+2\sqrt{ 58 } }{ 2 },\\x=\frac{ -14-2\sqrt{ 58 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=-7+\sqrt{ 58 },\\x=\frac{ -14-2\sqrt{ 58 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=-7+\sqrt{ 58 },\\x=-7-\sqrt{ 58 }\end{array}$

The equation has $2$ solutions

\begin{align*}&\begin{array} { l }x_1=-7-\sqrt{ 58 },& x_2=-7+\sqrt{ 58 }\end{array} \\&\begin{array} { l }x_1\approx-14.61577,& x_2\approx0.615773\end{array}\end{align*}

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