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June 4th, 2019, 08:49 PM  #1 
Newbie Joined: Jun 2019 From: Colorado Posts: 1 Thanks: 0  Order of Operations with sqrt
Looking for step by step guide of how to answer. Have a “maybe” answer but it does not look right... struggling with +/ and square root.
Last edited by skipjack; June 5th, 2019 at 08:12 AM. 
June 4th, 2019, 09:16 PM  #2 
Member Joined: Oct 2018 From: USA Posts: 88 Thanks: 61 Math Focus: Algebraic Geometry 
$x = \pm b$ just means that $x$ can be either positive $b$ or negative $b$. Similarly, $x \pm b$ just means both $x+b$ and $xb$. Starting with: $\displaystyle \frac{20 \pm \sqrt{20^{2}4(25)(4)}}{2(25)}$ $20^2 = 400$ and $4 \times 25 \times 4=400$ $\displaystyle \frac{20 \pm \sqrt{400400}}{2(25)}$ Now, the denominator, $2 \times 25 = 50$ $\displaystyle \frac{20 \pm \sqrt{400400}}{50}$ $400400 = 0$ and $\sqrt{0}=0$ $\displaystyle \frac{20 \pm 0}{50}$ Since its $\pm 0$ , adding and subtracting $0$ both do the same thing, so we will only have one $x$ value. $\displaystyle \frac{20 \pm 0}{50}=\frac{20}{50} = \frac{2}{5}$ So, we have $x=\frac{2}{5}$ P.S: This appears to be the quadratic formula for $25x^{2}+20x+4$, so now that we know the $x$ value, we know $25x^{2}+20x+4 = 0$ at $x=\frac{2}{5}$ Last edited by Greens; June 4th, 2019 at 09:17 PM. Reason: LaTeX 
June 23rd, 2019, 06:44 AM  #3  
Newbie Joined: Jun 2019 From: New York Posts: 23 Thanks: 0  Excellent Quote:
I check this myself and I can confirm that it correct.NinjaX3  
June 23rd, 2019, 01:11 PM  #4 
Member Joined: Oct 2018 From: USA Posts: 88 Thanks: 61 Math Focus: Algebraic Geometry 
Good news 
June 24th, 2019, 12:32 PM  #5 
Newbie Joined: Jun 2019 From: New York Posts: 23 Thanks: 0 
I am glad that this helped.

June 24th, 2019, 02:02 PM  #6 
Senior Member Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 
Just to clarify (since the original title was order of operations), you can think of $\displaystyle \sqrt {20^2  4(25)(4)}$ as $\displaystyle (20^2  4(25)(4))^{0.5}$. Taking the square root is just raising to a power, and takes the same priority. Simplify everything inside the radical, then take the root (if it simplifies), then continue on as normal (in this case, add or subtract from 20, and then divide by 50). 

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