Find the roots of the equation using the Quadratic Formula
$\frac{x^2+5+x+6}{x+1}=0$
2
Add the values $5$ and $6$
$\frac{11+x^2+x}{x+1}=0$
3
Multiply both sides of the equation by $x+1$
$11+x^2+x=0$
4
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 $c=11$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{-1\pm \sqrt{1-4\cdot 11}}{2}$
5
To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)
Verify that the solutions obtained are valid in the initial equation
14
The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.