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Chapter 1: Problem 4

Solve each equation in Exercises \(1-14\) by factoring. $$x^{2}=-11 x-10$$

Short Answer

Expert verified
The solution to the equation \(x^{2}=-11 x-10\) is \(x = -1, -10\).

Step by step solution

01

Rewrite the equation

Start with the given equation \(x^{2}=-11 x-10\). To rewrite this equation in the standard quadratic form \(ax^{2} + bx + c = 0\), add \(11x + 10\) to both sides to get \(x^{2} + 11x + 10 = 0\).
02

Factorize the equation

Now factorize the equations, looking for two numbers that add up to 11 (coefficient of x) and multiply to 10 (constant term). The numbers that meet this criteria are \(x+1\) and \(x+10\). So, the factored form of the equation is \((x + 1)(x + 10) = 0\).
03

Solve for x

Finally, solve for x by setting each factor equal to zero and solving. This gives \(x+1 = 0 \Rightarrow x = -1\) and \(x+10 = 0 \Rightarrow x = -10\).

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Most popular questions from this chapter

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