Question

How do you solve ${x^2} + 4x + 3 = 0$ using the quadratic formula?

Answer 1

Hint: A quadratic equation is an equation that could be written as $a{x^2} + bx + c = 0$. When using the quadratic formula, we should be aware of three possibilities. These three possibilities are distinguished by a part of the formula called the discriminant. The discriminant is the value under the radical sign, ${b^2} - 4ac$.

Formula used: $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$

Complete step by step answer:
For the quadratic equation $a{x^2} + bx + c = 0$ the formula for the roots is
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
Identify the values for $a,b,\& c$
${x^2} + 4x + c = 0$ comparing
  $a = 1,b = 4,c = 3$
Substitute these numbers into formula
$x = \dfrac{{ - 4 \pm \sqrt {{4^2} - (4 \times 1 \times 3)} }}{{2 \times 1}}$
Carefully proceed and do the calculations
$\Rightarrow$ $x = \dfrac{{ - 4 \pm \sqrt {16 - 12} }}{2}$
$\Rightarrow$ $x = \dfrac{{ - 4 \pm \sqrt 4 }}{2}$
$\Rightarrow$ $x = \dfrac{{ - 4 \pm 2}}{2}$
Now calculate the two separate solutions
$\Rightarrow$ ${x_1} = \dfrac{{ - 4 + 2}}{2} = \dfrac{{ - 2}}{2} = - 1$
$\Rightarrow$ ${x_2} = \dfrac{{ - 4 - 2}}{2} = - \dfrac{6}{2} = - 3$

Note: Solving quadratic equations can be difficult, but luckily there are several different methods that we can use depending on what type of quadratic that we are trying to solve. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square, and the quadratic formula.
Quadratic equations are polynomials, meaning strings of math terms.
Factoring
To solve a quadratic equation by factoring,
Put all terms on one side of the equal sign, leaving zero on the other side.
Factor.
Set each factor equal to zero.
Solve each of these equations.
Check by inserting your answer in the original equation.
The quadratic formula
Many quadratic equations cannot be solved by factoring. This is generally true when the roots, or answers, are not rational numbers. A second method of solving quadratic equations involves the use of the following formula:
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
a, b and c are taken from the quadratic equation written in its general form of
$a{x^2} + bx + c = 0$
where a is the numeral that goes in front of ${x^2}$, b is the numeral that goes in front of x, and c is the numeral with no variable next to it (a.k.a., “the constant”).