0=6.28r^2+1522.272r-27346.7544

Simple and best practice solution for 0=6.28r^2+1522.272r-27346.7544 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 0=6.28r^2+1522.272r-27346.7544 equation:


Simplifying
0 = 6.28r2 + 1522.272r + -27346.7544

Reorder the terms:
0 = -27346.7544 + 1522.272r + 6.28r2

Solving
0 = -27346.7544 + 1522.272r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 27346.7544 = 27346.7544
27346.7544 + -1522.272r + -6.28r2 = -27346.7544 + 1522.272r + 6.28r2 + 27346.7544 + -1522.272r + -6.28r2

Reorder the terms:
27346.7544 + -1522.272r + -6.28r2 = -27346.7544 + 27346.7544 + 1522.272r + -1522.272r + 6.28r2 + -6.28r2

Combine like terms: -27346.7544 + 27346.7544 = 0.0000
27346.7544 + -1522.272r + -6.28r2 = 0.0000 + 1522.272r + -1522.272r + 6.28r2 + -6.28r2
27346.7544 + -1522.272r + -6.28r2 = 1522.272r + -1522.272r + 6.28r2 + -6.28r2

Combine like terms: 1522.272r + -1522.272r = 0.000
27346.7544 + -1522.272r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
27346.7544 + -1522.272r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
27346.7544 + -1522.272r + -6.28r2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-4354.578726 + 242.4r + r2 = 0

Move the constant term to the right:

Add '4354.578726' to each side of the equation.
-4354.578726 + 242.4r + 4354.578726 + r2 = 0 + 4354.578726

Reorder the terms:
-4354.578726 + 4354.578726 + 242.4r + r2 = 0 + 4354.578726

Combine like terms: -4354.578726 + 4354.578726 = 0.000000
0.000000 + 242.4r + r2 = 0 + 4354.578726
242.4r + r2 = 0 + 4354.578726

Combine like terms: 0 + 4354.578726 = 4354.578726
242.4r + r2 = 4354.578726

The r term is 242.4r.  Take half its coefficient (121.2).
Square it (14689.44) and add it to both sides.

Add '14689.44' to each side of the equation.
242.4r + 14689.44 + r2 = 4354.578726 + 14689.44

Reorder the terms:
14689.44 + 242.4r + r2 = 4354.578726 + 14689.44

Combine like terms: 4354.578726 + 14689.44 = 19044.018726
14689.44 + 242.4r + r2 = 19044.018726

Factor a perfect square on the left side:
(r + 121.2)(r + 121.2) = 19044.018726

Calculate the square root of the right side: 138.000067848

Break this problem into two subproblems by setting 
(r + 121.2) equal to 138.000067848 and -138.000067848.

Subproblem 1

r + 121.2 = 138.000067848 Simplifying r + 121.2 = 138.000067848 Reorder the terms: 121.2 + r = 138.000067848 Solving 121.2 + r = 138.000067848 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.2' to each side of the equation. 121.2 + -121.2 + r = 138.000067848 + -121.2 Combine like terms: 121.2 + -121.2 = 0.0 0.0 + r = 138.000067848 + -121.2 r = 138.000067848 + -121.2 Combine like terms: 138.000067848 + -121.2 = 16.800067848 r = 16.800067848 Simplifying r = 16.800067848

Subproblem 2

r + 121.2 = -138.000067848 Simplifying r + 121.2 = -138.000067848 Reorder the terms: 121.2 + r = -138.000067848 Solving 121.2 + r = -138.000067848 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.2' to each side of the equation. 121.2 + -121.2 + r = -138.000067848 + -121.2 Combine like terms: 121.2 + -121.2 = 0.0 0.0 + r = -138.000067848 + -121.2 r = -138.000067848 + -121.2 Combine like terms: -138.000067848 + -121.2 = -259.200067848 r = -259.200067848 Simplifying r = -259.200067848

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16.800067848, -259.200067848}

See similar equations:

| A-5x=bforX | | 12x-22+7x+18+10x-6=180 | | 6x+3=2x+-9 | | 61=2x+5 | | 4(Q+3)+5Q=-33 | | -(2m-6)(-9m+6)=m-10-7m+10 | | -10=(s-8)/(-7) | | -5.5+3.5(1-9.5a)=25.5 | | .15x=3 | | 2p-7p+4c+1= | | 12c+7b+24= | | 6x-18+18=5x | | 28=7-(3/2t) | | -0.79x+24=1.19x | | y/246=27 | | 44+2a+(a+10)=180 | | Cos^-1(0.707/cos(3x)) | | 4(P+3)+5Q=-33 | | (Y/3)-6=4 | | 5f-8-4f=-28 | | 2(-1+3)-5(1+1)=3(-1-1) | | 2x+35=101 | | -10r-6(-5r-6)=2(-10-4r) | | 3e^2x+4=8 | | 17p-2p=4p+5 | | -8x-40=14-6x | | ×/5-2=2 | | (-4a-1)/10a=3/8 | | (-7,-8),m=-3/7 | | 5x+8=-3 | | -4v-8v-(-6v)=18 | | 0.8-(6-7.2)= |

Equations solver categories