Question

Solve the following quadratic equation: \[4{x^2} + 5x = 0\].

Answer 1

Hint: Use the technique of taking terms common from the given equation and then solve, then write the equation into simpler expressions and forms. Then after writing it into forms of factors in multiplied form, equate it to zero as given and get the solution.

Complete step-by-step solution:
We are given with the equation \[4{x^2} + 5x = 0\],
Then let us take \[x\]common from both the first and second term of the left hand side of the equation i.e.
\[x(4x + 5) = 0\]
So now each of the factors thus obtained is equal to the right hand side of the equation i.e. the left hand side is equal to the right hand side of the equation which is equal to zero, then:
\[x = 0,4x + 5 = 0\]
\[ \Rightarrow x = 0,x = \dfrac{{ - 5}}{4}\]
Therefore, the solution of the quadratic equation is \[x = 0,x = \dfrac{{ - 5}}{4}\].
Additional information: In mathematics, physics and in the study of quants a quadratic is a type of example that offers a variable extended via itself — an operation called squaring. This language derives from the vicinity of a square being its side length increased by way of itself. The word "quadratic" comes from quadratum derived from the Latin word which means square. Quadratic equations are virtually used in everyday life, as whilst calculating regions, figuring out a product's earnings or formulating the velocity of an item. Quadratic equations consult with equations with at least one squared variable, with the most standard form being. Quadratic equations are used to represent different functions, different real life processes and used in various fields like chemistry, biology, physics and many other fields to solve and get the desired solution.

Note: It is important that we know various ways, techniques, shortcuts and methods to solve different types of quadratic equations. Middle term factoring, Sridharacharya method or Quadratic formula, graphical methods are some techniques of solving the roots of a quadratic equation.