Question

given the equation $x^2 - 36 = $, solve for the solution by inspection. use the keypad to enter your answer in the box. additional symbols can be found using the drop - down arrows at the top of the keypad. - the value of $c$ in the quadratic equation is, $square$. - the solutions of the equation are: $x = square$ and $x = square$

Explanation:

Step1: Rewrite equation to standard form

First, rewrite the given equation \(x^2 - 36 = 0\) into the standard quadratic form \(ax^2 + bx + c = 0\). Here, \(a=1\), \(b=0\), so \(c = -36\).

Step2: Solve \(x^2 = 36\) by inspection

We find numbers whose square equals 36.
\(x^2 = 36\) implies \(x = \sqrt{36}\) or \(x = -\sqrt{36}\)

Step3: Calculate square roots

\(\sqrt{36}=6\), \(-\sqrt{36}=-6\)

Answer:

• The value of c in the quadratic equation is, \(-36\)
• The solutions of the equation are: \(x = 6\) and \(x = -6\)