Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?

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Question:

Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

Let

Rewrite the equation

Complete  the square

rewrite as perfect squares

square root both sides

the solutions are

u=-2,u=1

Alternative Method

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

Find the solutions of  the original equation

For u=-2

—->

For u=1

—->

therefore

The solutions of the original equation are

x=-5 and x=-2

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