Solve the Quadratic Equation: x²-19x+60=0 Step-by-Step

Question

x219x+60=0 x^2-19x+60=0

Video Solution

Solution Steps

00:00 Find X
00:03 We'll break it down using a trinomial, looking at coefficients
00:09 We want to find 2 numbers whose sum equals B (-19)
00:16 and their product equals C (60)
00:22 These are the matching numbers, we'll substitute in parentheses
00:31 We'll find what zeroes each factor
00:43 And this is the solution to the question

Step-by-Step Solution

Let's observe that the given equation:

x219x+60=0 x^2-19x+60=0 is a quadratic equation that can be solved using quick factoring:

x219x+60=0{??=60?+?=19(x4)(x15)=0 x^2-19x+60=0 \longleftrightarrow\begin{cases}\underline{?}\cdot\underline{?}=60\\ \underline{?}+\underline{?}=-19\end{cases}\\ \downarrow\\ (x-4)(x-15)=0 and therefore we get two simpler equations from which we can extract the solution:

(x4)(x15)=0x4=0x=4x15=0x=15x=4,15 (x-4)(x-15)=0 \\ \downarrow\\ x-4=0\rightarrow\boxed{x=4}\\ x-15=0\rightarrow\boxed{x=15}\\ \boxed{x=4,15} Therefore, the correct answer is answer A.

Answer

x=15,x=4 x=15,x=4