SOLUTION: can someone please help me solve by using the quadratic formula: 4r^2+4r=7 and 6x^2+53x=6x-35

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: can someone please help me solve by using the quadratic formula: 4r^2+4r=7 and 6x^2+53x=6x-35      Log On


   

Question 145389: can someone please help me solve by using the quadratic formula:
4r^2+4r=7 and 6x^2+53x=6x-35
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



4r%5E2%2B4r=7 Start with the given equation.


4r%5E2%2B4r-7=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=4, and c=-7


Let's use the quadratic formula to solve for r


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


r+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%284%29%28-7%29+%29%29%2F%282%284%29%29 Plug in a=4, b=4, and c=-7


r+=+%28-4+%2B-+sqrt%28+16-4%284%29%28-7%29+%29%29%2F%282%284%29%29 Square 4 to get 16.


r+=+%28-4+%2B-+sqrt%28+16--112+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-7%29 to get -112


r+=+%28-4+%2B-+sqrt%28+16%2B112+%29%29%2F%282%284%29%29 Rewrite sqrt%2816--112%29 as sqrt%2816%2B112%29


r+=+%28-4+%2B-+sqrt%28+128+%29%29%2F%282%284%29%29 Add 16 to 112 to get 128


r+=+%28-4+%2B-+sqrt%28+128+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


r+=+%28-4+%2B-+8%2Asqrt%282%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


r+=+%28-4%2B8%2Asqrt%282%29%29%2F%288%29 or r+=+%28-4-8%2Asqrt%282%29%29%2F%288%29 Break up the expression.


r+=+-1%2F2%2Bsqrt%282%29 or r+=+-1%2F2-sqrt%282%29 Reduce

So our answers are r+=+-1%2F2%2Bsqrt%282%29 or r+=+-1%2F2-sqrt%282%29


which approximate to r=0.914 or r=-1.914







# 2




6x%5E2%2B53x=6x-35 Start with the given equation.


6x%5E2%2B53x-6x%2B35=0 Get all terms to the left side.


6x%5E2%2B47x%2B35=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=6, b=47, and c=35


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-%2847%29+%2B-+sqrt%28+%2847%29%5E2-4%286%29%2835%29+%29%29%2F%282%286%29%29 Plug in a=6, b=47, and c=35


x+=+%28-47+%2B-+sqrt%28+2209-4%286%29%2835%29+%29%29%2F%282%286%29%29 Square 47 to get 2209.


x+=+%28-47+%2B-+sqrt%28+2209-840+%29%29%2F%282%286%29%29 Multiply 4%286%29%2835%29 to get 840


x+=+%28-47+%2B-+sqrt%28+1369+%29%29%2F%282%286%29%29 Subtract 840 from 2209 to get 1369


x+=+%28-47+%2B-+sqrt%28+1369+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-47+%2B-+37%29%2F%2812%29 Take the square root of 1369 to get 37.


x+=+%28-47+%2B+37%29%2F%2812%29 or x+=+%28-47+-+37%29%2F%2812%29 Break up the expression.


x+=+%28-10%29%2F%2812%29 or x+=++%28-84%29%2F%2812%29 Combine like terms.


x+=+-5%2F6 or x+=+-7 Simplify.


So our answers are x+=+-5%2F6 or x+=+-7