Solve the Quadratic Equation: x² - 5x - 50 = 0 Step-by-Step

Question

x2−5x−50=0 x^2-5x-50=0

Video Solution

Solution Steps

00:06 Let's find X in this equation.
00:09 We'll factor the trinomial. Let's examine the coefficients closely.
00:14 We need two numbers that add up to B, which is five.
00:21 They should also multiply to give C, which is negative fifty.
00:29 We found the numbers! Let's put them in the parentheses.
00:36 Now, let's see what makes each factor equal zero.
00:46 And that's how we solve for X in this problem!

Step-by-Step Solution

Let's observe that the given equation:

x2−5x−50=0 x^2-5x-50=0 is a quadratic equation that can be solved using quick factoring:

x2−5x−50=0⟷{?‾⋅?‾=−50?‾+?‾=−5↓(x−10)(x+5)=0 x^2-5x-50=0 \longleftrightarrow\begin{cases}\underline{?}\cdot\underline{?}=-50\\ \underline{?}+\underline{?}=-5\end{cases}\\ \downarrow\\ (x-10)(x+5)=0 and therefore we get two simpler equations from which we can extract the solution:

(x−10)(x+5)=0↓x−10=0→x=10x+5=0→x=−5x=10,−5 (x-10)(x+5)=0 \\ \downarrow\\ x-10=0\rightarrow\boxed{x=10}\\ x+5=0\rightarrow\boxed{x=-5}\\ \boxed{x=10,-5} Therefore, the correct answer is answer C.

Answer

x=10,x=−5 x=10,x=-5

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