5619.7a^2+94864a-47838000=0

Simple and best practice solution for 5619.7a^2+94864a-47838000=0 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 5619.7a^2+94864a-47838000=0 equation:


Simplifying
5619.7a2 + 94864a + -47838000 = 0

Reorder the terms:
-47838000 + 94864a + 5619.7a2 = 0

Solving
-47838000 + 94864a + 5619.7a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
5619.7 the coefficient of the squared term: 

Divide each side by '5619.7'.
-8512.554051 + 16.8806164a + a2 = 0

Move the constant term to the right:

Add '8512.554051' to each side of the equation.
-8512.554051 + 16.8806164a + 8512.554051 + a2 = 0 + 8512.554051

Reorder the terms:
-8512.554051 + 8512.554051 + 16.8806164a + a2 = 0 + 8512.554051

Combine like terms: -8512.554051 + 8512.554051 = 0.000000
0.000000 + 16.8806164a + a2 = 0 + 8512.554051
16.8806164a + a2 = 0 + 8512.554051

Combine like terms: 0 + 8512.554051 = 8512.554051
16.8806164a + a2 = 8512.554051

The a term is 16.8806164a.  Take half its coefficient (8.4403082).
Square it (71.23880251) and add it to both sides.

Add '71.23880251' to each side of the equation.
16.8806164a + 71.23880251 + a2 = 8512.554051 + 71.23880251

Reorder the terms:
71.23880251 + 16.8806164a + a2 = 8512.554051 + 71.23880251

Combine like terms: 8512.554051 + 71.23880251 = 8583.79285351
71.23880251 + 16.8806164a + a2 = 8583.79285351

Factor a perfect square on the left side:
(a + 8.4403082)(a + 8.4403082) = 8583.79285351

Calculate the square root of the right side: 92.648760669

Break this problem into two subproblems by setting 
(a + 8.4403082) equal to 92.648760669 and -92.648760669.

Subproblem 1

a + 8.4403082 = 92.648760669 Simplifying a + 8.4403082 = 92.648760669 Reorder the terms: 8.4403082 + a = 92.648760669 Solving 8.4403082 + a = 92.648760669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.4403082' to each side of the equation. 8.4403082 + -8.4403082 + a = 92.648760669 + -8.4403082 Combine like terms: 8.4403082 + -8.4403082 = 0.0000000 0.0000000 + a = 92.648760669 + -8.4403082 a = 92.648760669 + -8.4403082 Combine like terms: 92.648760669 + -8.4403082 = 84.208452469 a = 84.208452469 Simplifying a = 84.208452469

Subproblem 2

a + 8.4403082 = -92.648760669 Simplifying a + 8.4403082 = -92.648760669 Reorder the terms: 8.4403082 + a = -92.648760669 Solving 8.4403082 + a = -92.648760669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8.4403082' to each side of the equation. 8.4403082 + -8.4403082 + a = -92.648760669 + -8.4403082 Combine like terms: 8.4403082 + -8.4403082 = 0.0000000 0.0000000 + a = -92.648760669 + -8.4403082 a = -92.648760669 + -8.4403082 Combine like terms: -92.648760669 + -8.4403082 = -101.089068869 a = -101.089068869 Simplifying a = -101.089068869

Solution

The solution to the problem is based on the solutions from the subproblems. a = {84.208452469, -101.089068869}

See similar equations:

| 3w(10w+7)= | | 3x/2y+13x/6y | | 3/4(x+4)=81/4 | | 4x^2+45x+140=0 | | 5x^2+6y^2=30 | | 4k+26=6 | | 0=4(8)-7 | | N+13=10 | | (s+3)(s-12)= | | -1x+2y=1 | | b+1/5b=30 | | -10t^2+9t+90=0 | | 17/24-34=0 | | 17/2x-34=0 | | 3/4x*1=8 | | 5(3-4x)+5=5x | | -8y+4x=1 | | 2x+7y+3z=-25 | | 3x-12+4x+32=10-5x+15 | | (5n)/5=(25-4m)/5 | | 3x+1y=31 | | 5x^2+9x-20=0 | | V-5=7 | | -5x^2-9x+28=0 | | 5x-1+6x=3 | | (5y/4c^3k^2)+(k^3w/8c^2d) | | 1/3(d-4)-3/2(5d-3)=5/6 | | x=-16+4 | | 0.5=4(5x-3) | | 8x+5+7x-12=10x+113 | | log(4)(1/64) | | 9y-7.7=4.5 |

Equations solver categories