anonymous
  • anonymous
x2-8x=33 using factor formula and quadratic formula. I need help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Hint: x+3 is a factor.
anonymous
  • anonymous
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anonymous
  • anonymous
Solve it @Asuarez_7

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anonymous
  • anonymous
Thank you, can you help me on a other one?
anonymous
  • anonymous
49^2-1=0
anonymous
  • anonymous
wait,we haven't finish yet.. so what are values for x?
anonymous
  • anonymous
*are the
anonymous
  • anonymous
Is it 3?
anonymous
  • anonymous
Wait no it's x= 11 and x= -3
anonymous
  • anonymous
correct!
anonymous
  • anonymous
One important issue should be mentioned at this point: Just as with linear equations, the solutions to quadratic equations may be verified by plugging them back into the original equation, and making sure that they work, that they result in a true statement. For the above example, we would do the following:\[checking~x=-3~inn~(x+3)(x-11)=0:\]\[([-3]+3)([-3]-11)=0\]\[(0)(-14)=0\]\[0=0\]\[checking~x=11~inn~(x+3)(x-11)=0:\]\[([11]+3)([11]-11)=0\]\[(14)(0)=0\]\[0=0\]So both solutions "check" and are thus verified as being correct.
anonymous
  • anonymous
That was factorisation method,now let's use the quadratic formula to find the values for x
anonymous
  • anonymous
Solving using Quadratic Formula \[x ^{2}-8x=33 \] \[Ax ^{2}+Bx+C=0\] \[x^{2}-8x-33=0\] a=1 b=-8 c=-33 \[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\] \[x=\frac{ -(-8) \pm \sqrt{8^{2}-4(1)(-33)} }{ 2(1) }\] \[x=\frac{ 8 \pm \sqrt{64+132} }{ 2 }\] \[x=\frac{ 8 \pm \sqrt{196} }{ 2 }\] \[x=\frac{ 8 \pm 14 }{ 2 }\] \[x _{1}=\frac{ 8 + 14 }{ 2 }\] \[x _{1}=\frac{ 22 }{ 2 } =11\] \[x _{2}=\frac{ 8 - 14 }{ 2 }\] \[x _{2}=-\frac{ 6 }{ 2 } = -3\] Hope this helped..
anonymous
  • anonymous
Thanks it did but can you pls help me on this One using factoring and quadratic formula 49x^2-1=0
anonymous
  • anonymous
Factorisation: Difference of two squares:\[x^2-a^2=(x-a)(x+a)\]\[49x^2-1=0\]\[7^2x^2-1^1=0\]\[(7x-1)(7x+1)\]\[7x-1=0,7x+1=0\]\[7x=1,7x=-1\]
anonymous
  • anonymous
Then divide both sides by 7
anonymous
  • anonymous
\[\frac{ 7x }{ 7 }=\frac{ 1 }{ 7 }\]\[\frac{ 7x }{ 7 }=-\frac{ 1 }{ 7 }\]
anonymous
  • anonymous
so what are the values of x? @Asuarez_7
anonymous
  • anonymous
Is it 7?
anonymous
  • anonymous
no it is supposed to be\[x=\frac{ 1 }{ 7 }~and~x=-\frac{ 1 }{ 7 }\]
anonymous
  • anonymous
One important issue should be mentioned at this point: Just as with linear equations, the solutions to quadratic equations may be verified by plugging them back into the original equation, and making sure that they work, that they result in a true statement. For the above example, we would do the following:\[checking~x=\frac{ 1 }{ 7 }~inn~(7x-1)(7x+1)=0:\]\[(7[\frac{ 1 }{ 7 }]-1)(7[\frac{ 1 }{ 7 }]+1)=0\]\[(0)(2)=0\]\[0=0\]\[checking~x=-\frac{ 1 }{ 7 }~inn~(7x-1)(7x+1)=0:\]\[(7[-\frac{ 1 }{ 7 }]-1)(7[-\frac{ 1 }{ 7 }]+1)=0\]\[(-2)(0)=0\]\[0=0\]So both solutions "check" and are thus verified as being correct.

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