(x=5/2) 8=3x
8(x-5/2) -3x
Answers
Answer:
Rishi Gupta
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x+5)^2+x*(x/5+1)*(1-5*x)-2-(42*x/5-x*(x+5)^2+8*x^2/5)=0
Step by step solution :
STEP
1
:
x2
Simplify ——
5
Equation at the end of step
1
:
x x x2
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-(((42•—)-(x•((x+5)2)))+(8•——)) = 0
5 5 5
STEP
2
:
Equation at the end of step 2
x x 8x2
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-(((42•—)-x•(x+5)2)+———) = 0
5 5 5
STEP
3
:
x
Simplify —
5
Equation at the end of step
3
:
x x 8x2
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-(((42•—)-x•(x+5)2)+———) = 0
5 5 5
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
x • (x + 5)2 x • (x + 5)2 • 5
x • (x + 5)2 = ———————————— = ————————————————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
42x - (x • (x+5)2 • 5) -5x3 - 50x2 - 83x
—————————————————————— = —————————————————
5 5
Equation at the end of step
4
:
x (-5x3-50x2-83x) 8x2
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-(———————————————+———) = 0
5 5 5
STEP
5
:
STEP
6
:
Pulling out like terms :
6.1 Pull out like factors :
-5x3 - 50x2 - 83x = -x • (5x2 + 50x + 83)
Trying to factor by splitting the middle term
6.2 Factoring 5x2 + 50x + 83
The first term is, 5x2 its coefficient is 5 .
The middle term is, +50x its coefficient is 50 .
The last term, "the constant", is +83
Step-1 : Multiply the coefficient of the first term by the constant 5 • 83 = 415
Step-2 : Find two factors of 415 whose sum equals the coefficient of the middle term, which is 50 .
-415 + -1 = -416
-83 + -5 = -88
-5 + -83 = -88
-1 + -415 = -416
1 + 415 = 416
5 + 83 = 88
83 + 5 = 88
415 + 1 = 416
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions which have a common denominator :
6.3 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-x • (5x2+50x+83) + 8x2 -5x3 - 42x2 - 83x
——————————————————————— = —————————————————
5 5
Equation at the end of step
6
:
x (-5x3-42x2-83x)
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-——————————————— = 0
5 5
STEP
7
:
x
Simplify —
5
Equation at the end of step
7
:
x (-5x3-42x2-83x)
((((x+5)2)+((x•(—+1))•(1-5x)))-2)-——————————————— = 0
5 5
STEP
8
:
Rewriting the whole as an Equivalent Fraction :
8.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 5 as the denominator :
1 1 • 5
1 = — = —————
1 5
Adding fractions that have a common denominator :
8.2 Adding up the two equivalent fractions
:
Two solutions were found :
x = -1
x = -5