SOLUTION: Solve the following equations or inequalities: 3(x+2)-8=4(2-5x)+7 6x^2+7x=5 x^2+5x+7=0

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Question 172944: Solve the following equations or inequalities:
3(x+2)-8=4(2-5x)+7
6x^2+7x=5
x^2+5x+7=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.


# 1



3%28x%2B2%29-8=4%282-5x%29%2B7 Start with the given equation.


3x%2B6-8=8-20x%2B7 Distribute.


3x-2=8-20x%2B7 Combine like terms on the left side.


3x-2=-20x%2B15 Combine like terms on the right side.


3x=-20x%2B15%2B2 Add 2 to both sides.


3x%2B20x=15%2B2 Add 20x to both sides.


23x=15%2B2 Combine like terms on the left side.


23x=17 Combine like terms on the right side.


x=%2817%29%2F%2823%29 Divide both sides by 23 to isolate x.


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Answer:

So the answer is x=17%2F23 which approximates to x=0.739.






# 2




6x%5E2%2B7x=5 Start with the given equation.


6x%5E2%2B7x-5=0 Subtract 5 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=7, and c=-5


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-%287%29+%2B-+sqrt%28+%287%29%5E2-4%286%29%28-5%29+%29%29%2F%282%286%29%29 Plug in a=6, b=7, and c=-5


x+=+%28-7+%2B-+sqrt%28+49-4%286%29%28-5%29+%29%29%2F%282%286%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-5%29 to get -120


x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%286%29%29 Rewrite sqrt%2849--120%29 as sqrt%2849%2B120%29


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%286%29%29 Add 49 to 120 to get 169


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-7+%2B-+13%29%2F%2812%29 Take the square root of 169 to get 13.


x+=+%28-7+%2B+13%29%2F%2812%29 or x+=+%28-7+-+13%29%2F%2812%29 Break up the expression.


x+=+%286%29%2F%2812%29 or x+=++%28-20%29%2F%2812%29 Combine like terms.


x+=+1%2F2 or x+=+-5%2F3 Simplify.


So the answers are x+=+1%2F2 or x+=+-5%2F3