Question

How do you solve $25{x^2} - 30x = - 9$?

Answer 1

Hint: The Quadratic equation \[a{x^2} + bx + c = 0\], where "$a$", "\[b\]", and “c" are the "numerical coefficients" of the quadratic equation can be solved by using quadratic formula to solve. The Quadratic Formula is derived from the process of completing the square, and is formally stated as:
\[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\].

Complete step-by-step answer:
A quadratic equation is an equation which is written as, where a, b and c are coefficients, and this is the standard form of an equation, the quadratic formula which is given by,
$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$,
Given quadratic equation is,
$25{x^2} - 30x = - 9$,
The given equation should be rewritten in the standard form i.e.,\[a{x^2} + bx + c = 0\],
$ \Rightarrow 25{x^2} - 30x = - 9$,
Now add -9 to both sides of the equation we get,
$ \Rightarrow 25{x^2} - 30x + 9 = - 9 + 9$,
Now simplifying we get,
$ \Rightarrow 25{x^2} - 30x + 9 = 0$,
Now we got the equation in the standard form,
Now using the quadratic formula, i.e.,$x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$,
Here\[a = 25,b = - 30,c = 9\],
Now substituting the values in the formula we get,
$ \Rightarrow x = \dfrac{{ - ( - 30) \pm \sqrt {{{\left( { - 30} \right)}^2} - 4\left( {25} \right)\left( 9 \right)} }}{{2\left( {25} \right)}}$,
Now simplifying we get,
\[ \Rightarrow x = \dfrac{{30 \pm \sqrt {900 - \left( {900} \right)} }}{{50}}\],
Now again simplifying we get,
$ \Rightarrow x = \dfrac{{30 \pm \sqrt 0 }}{{50}}$,
Now taking the square root we get,
$ \Rightarrow x = \dfrac{{30}}{{50}}$,
Now simplifying we get,
$ \Rightarrow $$x = \dfrac{3}{5}$,
Now we get the value of $x$ it is $x = \dfrac{3}{5}$.
The value of the given equation is $\dfrac{3}{5}$.

If we solve the given equation, i.e.,$25{x^2} - 30x = - 9$, then the values for $x$ is $\dfrac{3}{5}$

Note:
Quadratic equation formula is a method of solving quadratic equations, and there are other methods to solve such kinds of solutions. Another method used to solve the quadratic equation is by factoring method, in this method we should obtain the solution factorising quadratic equation terms.