anonymous
  • anonymous
Find the solution set. √(x+24)-√(x-16)=4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
gabbyalicorn
  • gabbyalicorn
Let's solve your equation step-by-step. x+24−x−16=4 Step 1: Square both sides. (x+24)2−2x+24x−16+(x−16)2=16 x+24−2(x+24)(x−16)+x−16=16 −2x2+8x−384+2x+8=16 Step 2: Add -8 to both sides. −2x2+8x−384+2x+8+−8=16+−8 −2x2+8x−384+2x=8 Step 3: Add -2x to both sides. −2x2+8x−384+2x+−2x=8+−2x −2x2+8x−384=−2x+8 Step 4: Divide both sides by -2. −2x2+8x−384−2=−2x+8−2 x2+8x−384=x−4 Step 5: Solve Square Root. x2+8x−384=x−4 x2+8x−384=(x−4)2(Square both sides) x2+8x−384=x2−8x+16 x2+8x−384−x2=x2−8x+16−x2(Subtract x^2 from both sides) 8x−384=−8x+16 8x−384+8x=−8x+16+8x(Add 8x to both sides) 16x−384=16 16x−384+384=16+384(Add 384 to both sides) 16x=400 16x16=40016(Divide both sides by 16) x=25 Check answers. (Plug them in to make sure they work.) x=25(Works in original equation) Answer: x=25
anonymous
  • anonymous
love and appreciate the work but (x+4) and (x-16) are both in radicals. if you square everything you'd be down to x+24-x-16=16 or 8=16 because the x's cancel out. that's why I'm stuck on this problem
anonymous
  • anonymous
@touseii45 Umm, if you are squaring a sum of 2 different variables, then (x+y)^2 is NOT equal to x^2+y^2. You need to apply the formula x^2+y^2+2xy

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ParthKohli
  • ParthKohli
i think he copied the entire solution from somewhere but it is correct
anonymous
  • anonymous
@touseii45 if you do not believe what I wrote, then take any two numbers and you will see. for example 3^2+4^2 = 25, while (3+4)^2=49
anonymous
  • anonymous
i don't think i understand.
anonymous
  • anonymous
are you saying that √(x+24) being squared would be seen as x^2 + 24^2 and √(x-16) would be seen as x^2 -16^2 ?

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