Question

what is the positive solution of $x^2 - 36 = 5x$?

Explanation:

Step1: Rearrange the equation

First, we rearrange the given equation \(x^{2}-36 = 5x\) into standard quadratic form \(ax^{2}+bx + c=0\). Subtract \(5x\) from both sides:
\(x^{2}-5x - 36=0\)

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(- 36\) and add up to \(-5\). The numbers are \(-9\) and \(4\) since \((-9)\times4=-36\) and \(-9 + 4=-5\). So we can factor the quadratic as:
\((x - 9)(x+4)=0\)

Step3: Solve for \(x\)

Using the zero - product property, if \((x - 9)(x + 4)=0\), then either \(x-9=0\) or \(x + 4=0\).

• For \(x-9=0\), we get \(x = 9\).
• For \(x + 4=0\), we get \(x=-4\).

Step4: Identify the positive solution

We are asked for the positive solution. Among \(x = 9\) and \(x=-4\), the positive solution is \(x = 9\).

Answer:

\(9\)