8.57=0.021T^2+0.296T+3.803

Simple and best practice solution for 8.57=0.021T^2+0.296T+3.803 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 8.57=0.021T^2+0.296T+3.803 equation:


Simplifying
8.57 = 0.021T2 + 0.296T + 3.803

Reorder the terms:
8.57 = 3.803 + 0.296T + 0.021T2

Solving
8.57 = 3.803 + 0.296T + 0.021T2

Solving for variable 'T'.

Combine like terms: 8.57 + -3.803 = 4.767
4.767 + -0.296T + -0.021T2 = 3.803 + 0.296T + 0.021T2 + -3.803 + -0.296T + -0.021T2

Reorder the terms:
4.767 + -0.296T + -0.021T2 = 3.803 + -3.803 + 0.296T + -0.296T + 0.021T2 + -0.021T2

Combine like terms: 3.803 + -3.803 = 0.000
4.767 + -0.296T + -0.021T2 = 0.000 + 0.296T + -0.296T + 0.021T2 + -0.021T2
4.767 + -0.296T + -0.021T2 = 0.296T + -0.296T + 0.021T2 + -0.021T2

Combine like terms: 0.296T + -0.296T = 0.000
4.767 + -0.296T + -0.021T2 = 0.000 + 0.021T2 + -0.021T2
4.767 + -0.296T + -0.021T2 = 0.021T2 + -0.021T2

Combine like terms: 0.021T2 + -0.021T2 = 0.000
4.767 + -0.296T + -0.021T2 = 0.000

Begin completing the square.  Divide all terms by
-0.021 the coefficient of the squared term: 

Divide each side by '-0.021'.
-227 + 14.0952381T + T2 = 0

Move the constant term to the right:

Add '227' to each side of the equation.
-227 + 14.0952381T + 227 + T2 = 0 + 227

Reorder the terms:
-227 + 227 + 14.0952381T + T2 = 0 + 227

Combine like terms: -227 + 227 = 0
0 + 14.0952381T + T2 = 0 + 227
14.0952381T + T2 = 0 + 227

Combine like terms: 0 + 227 = 227
14.0952381T + T2 = 227

The T term is 14.0952381T.  Take half its coefficient (7.04761905).
Square it (49.66893427) and add it to both sides.

Add '49.66893427' to each side of the equation.
14.0952381T + 49.66893427 + T2 = 227 + 49.66893427

Reorder the terms:
49.66893427 + 14.0952381T + T2 = 227 + 49.66893427

Combine like terms: 227 + 49.66893427 = 276.66893427
49.66893427 + 14.0952381T + T2 = 276.66893427

Factor a perfect square on the left side:
(T + 7.04761905)(T + 7.04761905) = 276.66893427

Calculate the square root of the right side: 16.633368098

Break this problem into two subproblems by setting 
(T + 7.04761905) equal to 16.633368098 and -16.633368098.

Subproblem 1

T + 7.04761905 = 16.633368098 Simplifying T + 7.04761905 = 16.633368098 Reorder the terms: 7.04761905 + T = 16.633368098 Solving 7.04761905 + T = 16.633368098 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7.04761905' to each side of the equation. 7.04761905 + -7.04761905 + T = 16.633368098 + -7.04761905 Combine like terms: 7.04761905 + -7.04761905 = 0.00000000 0.00000000 + T = 16.633368098 + -7.04761905 T = 16.633368098 + -7.04761905 Combine like terms: 16.633368098 + -7.04761905 = 9.585749048 T = 9.585749048 Simplifying T = 9.585749048

Subproblem 2

T + 7.04761905 = -16.633368098 Simplifying T + 7.04761905 = -16.633368098 Reorder the terms: 7.04761905 + T = -16.633368098 Solving 7.04761905 + T = -16.633368098 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7.04761905' to each side of the equation. 7.04761905 + -7.04761905 + T = -16.633368098 + -7.04761905 Combine like terms: 7.04761905 + -7.04761905 = 0.00000000 0.00000000 + T = -16.633368098 + -7.04761905 T = -16.633368098 + -7.04761905 Combine like terms: -16.633368098 + -7.04761905 = -23.680987148 T = -23.680987148 Simplifying T = -23.680987148

Solution

The solution to the problem is based on the solutions from the subproblems. T = {9.585749048, -23.680987148}

See similar equations:

| 32=2(4+3X)+2(X+6) | | 6(3+4a)-2=160 | | 4m-2n+14=0 | | 8t+16.5=52.55 | | 3c^2+14x+8=0 | | 4-3x=-10 | | X^2+4x+9=9x+5 | | (-8c)+1=3 | | 13-8x=61-22x | | 3.14(17)= | | -4(2t-5)+2t=3t-8 | | 33-7x=2x+19 | | -2x-139=7x+68 | | -3x-40=64-11x | | 4x-16=50 | | x^3-6x^2-6=0 | | 16+5*3-30+10=X | | -5(10x-5)=325 | | 0=16t^2-25 | | -5(10x-5)=352 | | -8x+17= | | -58-8x=-178 | | 2x-54=65-5x | | 2sin^2(x)-1=0 | | (3x-1)(2x+5)-3(2x-1)(x+2)=24 | | 6y+2w+5y= | | 119-2x=16x+17 | | 119-2x=16x-17 | | 2sin^2x-3cosx=0 | | -11-11=13y-4-12y | | 3.14(21)= | | -14(x-6)= |

Equations solver categories