Question

How do you solve \[{x^2} - 361 = 0\]?

Answer 1

Hint: The Quadratic Formula uses the "\[a\]", "\[b\]", and "\[c\]" from \[a{x^2} + bx + c\], where "\[a\]", "\[b\]", and \[c\]c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you 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 solution:
Quadratic equations are the equations that are often called second degree. It means that it consists at least one term which is squared, the general form of quadratic equation is \[a{x^2} + bx + c = 0\], where "\[a\]", "\[b\]", and "\[c\]"are numerical coefficients or constant, and the value of \[x\] is unknown. And one fundamental rule is that the value of\[a\],the first constant cannot be zero in a quadratic equation.
Now the given quadratic equation is,
\[{x^2} - 361 = 0\],
Now using the quadratic formula, i.e, \[x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\],
Here \[a = 1,b = 0,c = - 361\],
Now substituting the values in the formula we get,
\[ \Rightarrow x = \dfrac{{ - 0 \pm \sqrt {{0^2} - 4\left( 1 \right)\left( { - 361} \right)} }}{{2\left( 1 \right)}}\],
Now simplifying we get,
\[ \Rightarrow x = \dfrac{{ \pm \sqrt {0 - \left( { - 1444} \right)} }}{2}\],
Now again simplifying we get,
\[ \Rightarrow x = \dfrac{{ \pm \sqrt {1444} }}{2}\],
Now taking the square root we get,
\[ \Rightarrow x = \dfrac{{ \pm 38}}{2}\],
Now we get two values of \[x\] they are \[x = 19,x = - 19\].
The two values of \[x\] for ten given equation are 19, and -19.

\[\therefore \]If we solve the given equation, i.e.,\[{x^2} - 361 = 0\], then the two values for x are 19 and -19.

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