Questions: The difference of the square of a number and 4 is equal to 3 times that number. Find the positive solution.

Transcript text: The difference of the square of a number and 4 is equal to 3 times that number. Find the positive solution.

Solution

Solution Steps

Step 1: Formulate the Equation

We start with the statement that the difference of the square of a number and 4 is equal to 3 times that number. This can be expressed mathematically as: \[ x^2 - 4 = 3x \]

Step 2: Rearrange the Equation

Rearranging the equation gives us a standard polynomial form: \[ x^2 - 3x - 4 = 0 \]

Step 3: Factor the Polynomial

Next, we factor the polynomial \(x^2 - 3x - 4\). The factorization results in: \[ (x - 4)(x + 1) = 0 \]

Step 4: Solve for \(x\)

Setting each factor equal to zero gives us the possible solutions: \[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \] \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \]

Step 5: Identify the Positive Solution

Among the solutions \(x = 4\) and \(x = -1\), the positive solution is: \[ x = 4 \]