OpenStudy (anonymous):

I NEED HELP! algebra solve the equation by factoring x^2=4x+12

3 years ago
OpenStudy (compassionate):

\(\Huge{\color{purple}{\textbf{W}} \color{orange}{\cal{E}} \color{green}{\mathbb{L}} \color{blue}{\mathsf{C}} \color{maroon}{\rm{O}} \color{red}{\tt{M}} \color{gold}{\tt{E}} \space \color{orchid}{\mathbf{T}} \color{Navy}{\mathsf{O}} \space \color{OrangeRed}{\boldsymbol{O}} \color{Olive}{\mathbf{P}} \color{Lime}{\textbf{E}} \color{DarkOrchid}{\mathsf{N}} \color{Tan}{\mathtt{S}} \color{magenta}{\mathbb{T}} \color{goldenrod}{\mathsf{U}} \color{ForestGreen}{\textbf{D}} \color{Salmon}{\mathsf{Y}} \ddot \smile }\) Here at OpenStudy Corp, we lead the user to the answer! The first step to solving this would be to factor all your terms on the right, to the left. \[x^2=4x+12 = x^2 - 4x - 12 = 0\] Alright, now we have: \[x^2 - 4x - 12\] The next step is to factor this into a binomial. A binoiam has the form: \[(x + y)(x + z)\] You've probably seen these before. Can you do the next step? (TIP: What two numbers, when added together, equal four, and when multiplied, equal twelve?) OpenStudy Ambassador; Compassionate.

3 years ago
OpenStudy (anonymous):

6 and -2?

3 years ago
OpenStudy (compassionate):

Correct! Actually, it would be two and negative six! :P Okay, so we know that the first term is x^2, right? So lets do that real fast: \[(x + ?)(x - ?)\] Are you familiar with the FOIL Method? First, Inner, Outer, Last. That is what we'll use to get our final product once we solve. Okay, so where does the two and negative six go? Can you guess? OpenStudy Ambassador; Compassionate.

3 years ago
OpenStudy (anonymous):

(x+2)(x-6)? that's my guess.

3 years ago
OpenStudy (compassionate):

Correct! Now lets FOIL that out to check our answer! F.O.I.L First \[ (x * x) = x^2\] Outer \[(-6 * x) = -6x\] Inner \[(2 * x) = 2x\] Last \[(2 * - 6) = -12\] So, we end up with: \[x^2 - 6x + 2x - 12\rightarrow x^2 - 4x - 12\] (Upon adding the common terms -6x and 2x) I hope this helped! Thank you for using OpenStudy, and we look forward to seeing you again. If you have any questions or concerns, feel free to private message me, or any Ambassador (The guys with the purple A's) or moderators (The guys with the purple NAMES). In compassionate and love, OpenStudy Ambassador; Compassionate.

3 years ago
OpenStudy (anonymous):

Thank You! :D

3 years ago