QuestionJune 6, 2025

Solve the equation by factoring: x^2-5x-6=0 x= 2,-3 x= -2,3 x= -1,6 x= 6,1

Solve the equation by factoring: x^2-5x-6=0 x= 2,-3 x= -2,3 x= -1,6 x= 6,1
Solve the equation by factoring: x^2-5x-6=0 x= 2,-3 x= -2,3 x= -1,6 x= 6,1

Solution
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Answer

x = \{6, -1\} Explanation 1. Identify the quadratic equation The given equation is x^2 - 5x - 6 = 0. 2. Factor the quadratic equation Find two numbers that multiply to -6 (constant term) and add to -5 (coefficient of x). These numbers are -6 and 1. Thus, factor as (x - 6)(x + 1) = 0. 3. Solve for x Set each factor equal to zero: x - 6 = 0 or x + 1 = 0. Solving these gives x = 6 or x = -1.

Explanation

1. Identify the quadratic equation<br /> The given equation is $x^2 - 5x - 6 = 0$.<br /><br />2. Factor the quadratic equation<br /> Find two numbers that multiply to $-6$ (constant term) and add to $-5$ (coefficient of $x$). These numbers are $-6$ and $1$. Thus, factor as $(x - 6)(x + 1) = 0$.<br /><br />3. Solve for $x$<br /> Set each factor equal to zero: $x - 6 = 0$ or $x + 1 = 0$. Solving these gives $x = 6$ or $x = -1$.
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