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Solve the quadratic equation
x^(2)-x-6=0 by factoring

Solve the quadratic equation $x^{2}-x-6=0$ by factoring

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Quadratic equation with complex roots

Full solution

Q. Solve the quadratic equation

x^{2}-x-6=0

by factoring

Identify coefficients: Step $1$ : Identify the coefficients of the quadratic equation $x^2 - x - 6 = 0$ . $a = 1$ , $b = -1$ , $c = -6$
Find multiplication factors: Step $2$ : Look for two numbers that multiply to $ac$ ( $1\times(-6) = -6$ ) and add to $b$ ( $-1$ ). $\newline$ Factors of $-6$ that add up to $-1$ are $-3$ and $2$ .
Rewrite middle term: Step $3$ : Rewrite the middle term using the factors found. $\newline$ $x^2 - 3x + 2x - 6 = 0$
Factor by grouping: Step $4$ : Factor by grouping. $\newline$ Group the terms: $(x^2 - 3x) + (2x - 6) = 0$ . $\newline$ Factor out the common terms: $x(x - 3) + 2(x - 3) = 0$
Factor out common factor: Step $5$ : Factor out the common binomial factor. $\newline$ $(x + 2)(x - 3) = 0$
Set equal and solve: Step $6$ : Set each factor equal to zero and solve for $x$ . $x + 2 = 0 \rightarrow x = -2$ $x - 3 = 0 \rightarrow x = 3$

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