SOLUTION: I have another two questions. This is confusing to me too. please help me. 3.) What value should be added to the expression to create a perfect square? x2 - 20x

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Question 195102: I have another two questions. This is confusing to me too. please help me.


3.) What value should be added to the expression to create a perfect square?
x2 - 20x



4. Solve.
x2 + 8x 8 = 0

Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
3)

x%5E2-20x Start with the given expression


Now take half of the x coefficient and square it to get %28-20%2F2%29%5E2=%28-10%29%5E2=100. This is the value that you add to the expression to make it a perfect square.

So x%5E2-20x%2B100 is a perfect square.




4)

Is the equation x%5E2%2B8x%2B8=0 ???



x%5E2%2B8x%2B8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=8, and c=8


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=8


x+=+%28-8+%2B-+sqrt%28+64-4%281%29%288%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-32+%29%29%2F%282%281%29%29 Multiply 4%281%29%288%29 to get 32


x+=+%28-8+%2B-+sqrt%28+32+%29%29%2F%282%281%29%29 Subtract 32 from 64 to get 32


x+=+%28-8+%2B-+sqrt%28+32+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-8+%2B-+4%2Asqrt%282%29%29%2F%282%29 Simplify the square root


x+=+%28-8%29%2F%282%29+%2B-+%284%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+-4+%2B-+2%2Asqrt%282%29 Reduce.


x+=+-4%2B2%2Asqrt%282%29 or x+=+-4-2%2Asqrt%282%29 Break up the expression.


So the answers are x+=+-4%2B2%2Asqrt%282%29 or x+=+-4-2%2Asqrt%282%29


which approximate to x=-1.172 or x=-6.828


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OR....

Is the equation x%5E2%2B8x-8=0 ???




x%5E2%2B8x-8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=8, and c=-8


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=-8


x+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64--32+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-8%29 to get -32


x+=+%28-8+%2B-+sqrt%28+64%2B32+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--32%29 as sqrt%2864%2B32%29


x+=+%28-8+%2B-+sqrt%28+96+%29%29%2F%282%281%29%29 Add 64 to 32 to get 96


x+=+%28-8+%2B-+sqrt%28+96+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-8+%2B-+4%2Asqrt%286%29%29%2F%282%29 Simplify the square root


x+=+%28-8%29%2F%282%29+%2B-+%284%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+-4+%2B-+2%2Asqrt%286%29 Reduce.


x+=+-4%2B2%2Asqrt%286%29 or x+=+-4-2%2Asqrt%286%29 Break up the expression.


So the answers are x+=+-4%2B2%2Asqrt%286%29 or x+=+-4-2%2Asqrt%286%29


which approximate to x=0.899 or x=-8.899