159.3864=6.28r+6.28r^2*6.7

Simple and best practice solution for 159.3864=6.28r+6.28r^2*6.7 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 159.3864=6.28r+6.28r^2*6.7 equation:


Simplifying
159.3864 = 6.28r + 6.28r2 * 6.7

Reorder the terms for easier multiplication:
159.3864 = 6.28r + 6.28 * 6.7r2

Multiply 6.28 * 6.7
159.3864 = 6.28r + 42.076r2

Solving
159.3864 = 6.28r + 42.076r2

Solving for variable 'r'.

Reorder the terms:
159.3864 + -6.28r + -42.076r2 = 6.28r + -6.28r + 42.076r2 + -42.076r2

Combine like terms: 6.28r + -6.28r = 0.00
159.3864 + -6.28r + -42.076r2 = 0.00 + 42.076r2 + -42.076r2
159.3864 + -6.28r + -42.076r2 = 42.076r2 + -42.076r2

Combine like terms: 42.076r2 + -42.076r2 = 0.000
159.3864 + -6.28r + -42.076r2 = 0.000

Begin completing the square.  Divide all terms by
-42.076 the coefficient of the squared term: 

Divide each side by '-42.076'.
-3.788059701 + 0.1492537313r + r2 = 0

Move the constant term to the right:

Add '3.788059701' to each side of the equation.
-3.788059701 + 0.1492537313r + 3.788059701 + r2 = 0 + 3.788059701

Reorder the terms:
-3.788059701 + 3.788059701 + 0.1492537313r + r2 = 0 + 3.788059701

Combine like terms: -3.788059701 + 3.788059701 = 0.000000000
0.000000000 + 0.1492537313r + r2 = 0 + 3.788059701
0.1492537313r + r2 = 0 + 3.788059701

Combine like terms: 0 + 3.788059701 = 3.788059701
0.1492537313r + r2 = 3.788059701

The r term is 0.1492537313r.  Take half its coefficient (0.07462686565).
Square it (0.005569169077) and add it to both sides.

Add '0.005569169077' to each side of the equation.
0.1492537313r + 0.005569169077 + r2 = 3.788059701 + 0.005569169077

Reorder the terms:
0.005569169077 + 0.1492537313r + r2 = 3.788059701 + 0.005569169077

Combine like terms: 3.788059701 + 0.005569169077 = 3.793628870077
0.005569169077 + 0.1492537313r + r2 = 3.793628870077

Factor a perfect square on the left side:
(r + 0.07462686565)(r + 0.07462686565) = 3.793628870077

Calculate the square root of the right side: 1.947724023

Break this problem into two subproblems by setting 
(r + 0.07462686565) equal to 1.947724023 and -1.947724023.

Subproblem 1

r + 0.07462686565 = 1.947724023 Simplifying r + 0.07462686565 = 1.947724023 Reorder the terms: 0.07462686565 + r = 1.947724023 Solving 0.07462686565 + r = 1.947724023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.07462686565' to each side of the equation. 0.07462686565 + -0.07462686565 + r = 1.947724023 + -0.07462686565 Combine like terms: 0.07462686565 + -0.07462686565 = 0.00000000000 0.00000000000 + r = 1.947724023 + -0.07462686565 r = 1.947724023 + -0.07462686565 Combine like terms: 1.947724023 + -0.07462686565 = 1.87309715735 r = 1.87309715735 Simplifying r = 1.87309715735

Subproblem 2

r + 0.07462686565 = -1.947724023 Simplifying r + 0.07462686565 = -1.947724023 Reorder the terms: 0.07462686565 + r = -1.947724023 Solving 0.07462686565 + r = -1.947724023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.07462686565' to each side of the equation. 0.07462686565 + -0.07462686565 + r = -1.947724023 + -0.07462686565 Combine like terms: 0.07462686565 + -0.07462686565 = 0.00000000000 0.00000000000 + r = -1.947724023 + -0.07462686565 r = -1.947724023 + -0.07462686565 Combine like terms: -1.947724023 + -0.07462686565 = -2.02235088865 r = -2.02235088865 Simplifying r = -2.02235088865

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.87309715735, -2.02235088865}

See similar equations:

| -4w^2+32w=-196 | | 39/130 | | .2((-11)+50)-6=.4(3(-11)+20) | | 4t+5x=5 | | -[7z-(10z+10)]=10+(2z+7) | | -6x+3=4+6x | | 13/26 | | 6-3x=22-x | | 2g-3=-10 | | 2w+4-w=19 | | -16x^3-4x^2=0 | | z^2+26z=43 | | 7x+8(x-3)=-9 | | 6=-3(1+7x)-6x | | 6(x+2)-4=4x+2(4+x) | | 8(y-2)=4.5(y-2) | | -8x-y=16 | | 72+4-14c=26 | | 37=8(y+4)-3y | | 12(x-7)-10=22x-154 | | f^2-8f-39=0 | | 1.6-0.9w=11.6+2.4w | | -35=-7u+5(u-3) | | -12(10n+5)=-10(n-6) | | 5[3(x+4)-2(1-4)]-x-35=14x+45 | | 2r^2-44r=-38 | | 5-1x-1x=-1 | | .25x=225 | | xy-9x+y=13 | | 2x+4xln(x)=4 | | .02(x+50)-6=.4(3x+20) | | 1/3y9 |

Equations solver categories