Solved example of equations with square roots
We need to isolate the dependent variable , we can do that by simultaneously subtracting $\sqrt{x+7}$ from both sides of the equation
Removing the variable's exponent raising both sides of the equation to the power of $2$
Divide $1$ by $\frac{1}{2}$
Simplify $\left(\sqrt{x}\right)^{2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $2$
Multiply $\frac{1}{2}$ times $2$
Multiply $\frac{1}{2}$ times $2$
Divide $1$ by $\frac{1}{2}$
Removing the variable's exponent raising both sides of the equation to the power of $2$
Square of the first term: $\left(7\right)^2 = .
Double product of the first by the second: $2\left(7\right)\left(-\sqrt{x+7}\right) = .
Square of the second term: $\left(-\sqrt{x+7}\right)^2 =
Expand $\left(7-\sqrt{x+7}\right)^{2}$
Simplify $\left(-\sqrt{x+7}\right)^2$
Simplify $\left(\sqrt{x+7}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $2$
Expand $\left(7-\sqrt{x+7}\right)^{2}$
Add the values $49$ and $7$
Move the term with the square root to the left side of the equation, and all other terms to the right side. Remember to change the signs of each term
Cancel like terms $x$ and $-x$
Removing the variable's exponent raising both sides of the equation to the power of $2$
Divide $1$ by $\frac{1}{2}$
Divide $1$ by $\frac{1}{2}$
Calculate the power $56^{2}$
Removing the variable's exponent raising both sides of the equation to the power of $2$
The power of a product is equal to the product of it's factors raised to the same power
Calculate the power $14^{2}$
Simplify $\left(\sqrt{x}\right)^{2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $2$
Multiply $\frac{1}{2}$ times $2$
Simplify $\left(\sqrt{x+7}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $2$
Multiply $\frac{1}{2}$ times $2$
Simplify $\left(\sqrt{x+7}\right)^{2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $\frac{1}{2}$ and $n$ equals $2$
Multiply $\frac{1}{2}$ times $2$
Multiply $\frac{1}{2}$ times $2$
The power of a product is equal to the product of it's factors raised to the same power
Divide both sides of the equation by $196$
Simplifying the quotients
Divide $3136$ by $196$
We need to isolate the dependent variable , we can do that by simultaneously subtracting $7$ from both sides of the equation
Subtract the values $16$ and $-7$
We need to isolate the dependent variable , we can do that by simultaneously subtracting $7$ from both sides of the equation
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the equation are the ones that, when replaced in the original equation, don't result in any square root of a negative number and make both sides of the equation equal to each other
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