Here, we show you a step-by-step solved example of equations with square roots. This solution was automatically generated by our smart calculator:
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $\sqrt{x-1}$ from both sides of the equation
Removing the variable's exponent raising both sides of the equation to the power of
Cancel exponents $\frac{1}{2}$ and $2$
Square of the first term: $\left(5\right)^2 = .
Double product of the first by the second: $2\left(5\right)\left(-\sqrt{x-1}\right) = .
Square of the second term: $\left(-\sqrt{x-1}\right)^2 =
Expand $\left(5-\sqrt{x-1}\right)^2$
Simplify $\left(-\sqrt{x-1}\right)^2$
Simplify $\left(\sqrt{x-1}\right)^2$ 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 $\left(5-\sqrt{x-1}\right)^2$
Cancel exponents $\frac{1}{2}$ and $2$
Subtract the values $25$ and $-1$
Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side
Subtract the values $24$ and $-4$
Cancel like terms $x$ and $-x$
Removing the variable's exponent raising both sides of the equation to the power of
Divide fractions $\frac{1}{\frac{1}{2}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$
Divide fractions $\frac{1}{\frac{1}{2}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$
Calculate the power $20^2$
The power of a product is equal to the product of it's factors raised to the same power
Calculate the power $10^2$
The power of a product is equal to the product of it's factors raised to the same power
Cancel exponents $\frac{1}{2}$ and $2$
Solve the product $100\left(x-1\right)$
Multiply $100$ times $-1$
Solve the product $100\left(x-1\right)$
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-100$ from both sides of the equation
Add the values $400$ and $100$
Divide both sides of the equation by $100$
Divide $500$ by $100$
Divide both sides of the equation by $100$
Simplify the fraction $\frac{100x}{100}$ by $100$
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