Use the method described in Exercises 83–86, if applicable, and p...

Question

Use the method described in Exercises 83–86, if applicable, and properties of
absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can
be solved by inspection.) | x^2 + 5x + 5 | = 1

Accepted Answer

Hello everyone. We're going to solve the equation. The absolute value of X squared plus seven. X plus eight equals two. So first recall that when we have an absolute value we have to set up two equations. So in this case that will be X squared plus seven. X plus eight equals positive two. And we need to set it up so it equals the opposite of the answer. So that would be a negative two. So we have X squared plus seven. X plus eight equals negative two. We're gonna solve each of these independently and the answers should give us all of our X values. So being a quadratic I recall that I want this to equal zero. So X squared plus seven X plus eight equals two. I'm going to subtract two from both sides to make it equal zero. So now I have X squared plus seven X Plus six equals 0. And that quadratic looks factory ble so we're going to factor it. It's gonna be an X plus six and then X plus one. X plus six times X plus one equals zero. To solve we set each set of parentheses equal to zero. So X plus six equals zero. X plus one equals zero. Subtracting six from both sides. For that one I get X equals negative six and for X plus one equals zero subtract one from both sides. X also equals -1. So we're about halfway there we know X could be negative six or negative one but now we need to solve our other equation. So X squared plus seven. X plus eight equals negative two. Again since it's quadratic, I want it to be equal to zero. So I'm gonna add two to both sides. And that gives me X squared plus seven. X plus 10 equals zero. And this one does look factory ble also so it looks like it's an X plus five and an X plus two. X plus five times X plus two equals zero. To find out what X equals. We set each set of parentheses equal to zero. So X plus five equals zero. X plus two equals zero. For X plus five equals zero. I subtract five from both sides. X equals negative five for X plus two equals zero. I subtract two from both sides And get x equals -2. So we now have all of our X values and so now we're gonna we need to look for our solution set in our answer choices. So I have a negative six A negative five a negative two and a negative one. And that matches answer choice B. Have a nice day

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | x^2 + 5x + 5 | = 1