# Calculate: sqrt(5u+14)=u

## Expression: $\sqrt{ 5u+14 }=u$

Square both sides of the equation

$5u+14={u}^{2}$

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

$5u+14-{u}^{2}=0$

Use the commutative property to reorder the terms

$-{u}^{2}+5u+14=0$

Change the signs on both sides of the equation

${u}^{2}-5u-14=0$

Write $-5u$ as a difference

${u}^{2}+2u-7u-14=0$

Factor out $u$ from the expression

$u \times \left( u+2 \right)-7u-14=0$

Factor out $-7$ from the expression

$u \times \left( u+2 \right)-7\left( u+2 \right)=0$

Factor out $u+2$ from the expression

$\left( u+2 \right) \times \left( u-7 \right)=0$

When the product of factors equals $0$, at least one factor is $0$

$\begin{array} { l }u+2=0,\\u-7=0\end{array}$

Solve the equation for $u$

$\begin{array} { l }u=-2,\\u-7=0\end{array}$

Solve the equation for $u$

$\begin{array} { l }u=-2,\\u=7\end{array}$

Check if the given value is the solution of the equation

$\begin{array} { l }\sqrt{ 5 \times \left( -2 \right)+14 }=-2,\\u=7\end{array}$

Check if the given value is the solution of the equation

$\begin{array} { l }\sqrt{ 5 \times \left( -2 \right)+14 }=-2,\\\sqrt{ 5 \times 7+14 }=7\end{array}$

Simplify the expression

$\begin{array} { l }2=-2,\\\sqrt{ 5 \times 7+14 }=7\end{array}$

Simplify the expression

$\begin{array} { l }2=-2,\\7=7\end{array}$

The equality is false, therefore $u=-2$ is not a solution of the equation

$\begin{array} { l }u≠-2,\\7=7\end{array}$

The equality is true, therefore $u=7$ is a solution of the equation

$\begin{array} { l }u≠-2,\\u=7\end{array}$

The equation has one solution

$u=7$

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