Here, we show you a step-by-step solved example of equations with square roots. This solution was automatically generated by our smart calculator:
Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{0.5}$
Cancel exponents $0.5$ and $1$
Cancel exponents $0.5$ and $1$
Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{0.5}$
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
Add the values $2$ and $1$
Rewrite the equation
To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-1$ and $c=-3$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Simplifying
Multiply $-1$ times $-1$
Multiply $-4$ times $-3$
Calculate the power ${\left(-1\right)}^2$
Add the values $1$ and $12$
Simplifying
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Combining all solutions, the $2$ solutions of the equation are
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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