Final Answer
Step-by-step Solution
Specify the solving method
A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$
Combining like terms $x^2$ and $x^2$
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 $3$ and $-1$
Factor the polynomial $2x^2-2x$ by it's greatest common factor (GCF): $2x$
Divide both sides of the equation by $2$
Simplifying the quotients
Divide $2$ by $2$
Solve the product $x\left(x-1\right)$
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 $c=-1$. 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
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Subtract the values $1$ and $-\sqrt{5}$
Add the values $1$ and $\sqrt{5}$
Divide $3.236068$ by $2$
Divide $-1.236068$ by $2$
Combining all solutions, the $2$ solutions of the equation are