Question

Solve the quadratic equation $2{x^2} + x - 4 = 0$ by completing the square.

Answer 1

Hint:
Here we have a quadratic equation. We will use some logic and some formulas for solving this question. Solving this equation for completing squares. Answers should have a quadratic equation format. This answer will be plus or minus values.

Complete step by step solution:
The given quadratic equation is
$2{x^2} + x - 4 = 0$
We will be divided by $2$ both sides we will get
${x^2} + \dfrac{x}{2} - 2 = 0$
Here, number two is going to right hand side
${x^2} + \dfrac{x}{2} = 2$
On adding both sides $\dfrac{1}{{16}}$ we will get
${x^2} + \dfrac{x}{2} + \dfrac{1}{{16}} = 2 + \dfrac{1}{{16}}$
The above equation is same like as formula
$ \Rightarrow {(x + \dfrac{1}{4})^2} = \dfrac{{32}}{{16}}$
We will take square root for both sides we will get the equation,
$ \Rightarrow x + \dfrac{1}{4} = \pm \dfrac{{\sqrt {33} }}{4}$
In left hand side $ + \dfrac{1}{4}$ is going to right hand side we will get
\[x = \pm \dfrac{{\sqrt {33} }}{4} - \dfrac{1}{4}\]
$\therefore $ finally, we will get the answer for this question is
$ \Rightarrow x = \dfrac{{ - 1 - \sqrt {33} }}{4}$ or $x = \dfrac{{ - 1 + \sqrt {33} }}{4}$
This is the answer for the above question.

Additional information:
Solving quadratic equations can sometimes be quite difficult. However, there are several different methods that can be used depending on the type of quadratic that needs to be solved. There are mainly four ways of solving a quadratic equation. They are factoring, using the square roots, completing the square and using the quadratic formula.

Note:
A quadratic equation is said to be any polynomial equation of degree $2$ or an equation that is in the form of, where \[a,{\text{ }}b\], and $c$ are coefficients. Then the quadratic formula, on the other hand $\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$ is a formula that is used for solving the quadratic equation. The formula is used to determine the roots/solutions to the equation.