Question

how many real solutions does the equation have?
d² - 12 = 73
no real solution one real solution
two real solutions

Explanation:

Step1: Solve for \(d^2\)

Add 12 to both sides of the equation \(d^2 - 12 = 73\).
\(d^2 - 12 + 12 = 73 + 12\)
\(d^2 = 85\)

Step2: Analyze the solutions for \(d\)

For an equation of the form \(x^2 = a\) (where \(a>0\)), there are two real solutions: \(x=\sqrt{a}\) and \(x = -\sqrt{a}\). Since \(85>0\), the equation \(d^2 = 85\) will have two real solutions: \(d=\sqrt{85}\) and \(d = -\sqrt{85}\).

Answer:

two real solutions