Question

darren chose to do the following steps to solve the equation. explain in your own words how darren found the two answers to the quadratic equation $x^{2}+4 = 104$. use the sketchpad if needed to support your explanation.

Explanation:

First, isolate the squared variable term by subtracting 4 from both sides of the equation to get \(x^2\) alone. Then, take the square root of both sides; since squaring a positive and negative number gives the same positive result, there will be two solutions: one positive and one negative.

Answer:

1. Subtract 4 from both sides of \(x^2 + 4 = 104\):

\(x^2 + 4 - 4 = 104 - 4\) simplifies to \(x^2 = 100\)

1. Take the square root of both sides:

\(x = \sqrt{100}\) and \(x = -\sqrt{100}\), so \(x = 10\) and \(x = -10\)
Darren isolated \(x^2\) first, then used the property that square roots have positive and negative values to find the two solutions 10 and -10.