Question

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

Explanation:

Step1: Rearrange the equation

We start with the equation \(x^2 - 36 = 5x\). To solve it, we first rearrange it into standard quadratic form \(ax^2+bx + c = 0\). Subtract \(5x\) from both sides:
\(x^2-5x - 36=0\)

Step2: Factor the quadratic

We need to find two numbers that multiply to \(- 36\) and add up to \(-5\). The numbers are \(-9\) and \(4\) because \(-9\times4=-36\) 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 \(ab = 0\), then either \(a = 0\) or \(b = 0\). So we set each factor equal to zero:

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

We are looking for the positive solution, so we consider \(x = 9\).

Answer:

\(9\)