SOLUTION: I'm at the beginning of college algebra, I have decent experience in algebra yet I have a hard time solving this among quadratic equations: 2(x+4)^2+18=0 Do I use the distributi

Question 1137983: I'm at the beginning of college algebra, I have decent experience in algebra yet I have a hard time solving this among quadratic equations: 2(x+4)^2+18=0
Do I use the distributive property before using the quadratic formula? thanks in advance.
Found 3 solutions by josgarithmetic, Boreal, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Simple Algebra, and expect complex solutions.

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is vertex form, so the vertex is (-h, k), where h is the number in parentheses and k is the constant. If the vertex is (-4, 18), we know that the minimum is above the x-axis and any roots will be imaginary.
It is also part of completing the square, which we use to solve:
to solve
(x+4)^2=-9
x+4=+/- 3i,taking square root of both sides
x=-4+/-3i, are the two roots.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

For introductory lessons on quadratic equations, look into these lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples
    - Solving quadratic equations without quadratic formula
    - Who is who in quadratic equations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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Be aware :   the solution by @josgarithmetic is   W R O N G !

For your safety, simply ignore it !

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