-a^2+30+40a=5+4a

Simple and best practice solution for -a^2+30+40a=5+4a 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 -a^2+30+40a=5+4a equation:


Simplifying
-1a2 + 30 + 40a = 5 + 4a

Reorder the terms:
30 + 40a + -1a2 = 5 + 4a

Solving
30 + 40a + -1a2 = 5 + 4a

Solving for variable 'a'.

Reorder the terms:
30 + -5 + 40a + -4a + -1a2 = 5 + 4a + -5 + -4a

Combine like terms: 30 + -5 = 25
25 + 40a + -4a + -1a2 = 5 + 4a + -5 + -4a

Combine like terms: 40a + -4a = 36a
25 + 36a + -1a2 = 5 + 4a + -5 + -4a

Reorder the terms:
25 + 36a + -1a2 = 5 + -5 + 4a + -4a

Combine like terms: 5 + -5 = 0
25 + 36a + -1a2 = 0 + 4a + -4a
25 + 36a + -1a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
25 + 36a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-25 + -36a + a2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -36a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + -36a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -36a + a2 = 0 + 25
-36a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
-36a + a2 = 25

The a term is -36a.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36a + 324 + a2 = 25 + 324

Reorder the terms:
324 + -36a + a2 = 25 + 324

Combine like terms: 25 + 324 = 349
324 + -36a + a2 = 349

Factor a perfect square on the left side:
(a + -18)(a + -18) = 349

Calculate the square root of the right side: 18.681541692

Break this problem into two subproblems by setting 
(a + -18) equal to 18.681541692 and -18.681541692.

Subproblem 1

a + -18 = 18.681541692 Simplifying a + -18 = 18.681541692 Reorder the terms: -18 + a = 18.681541692 Solving -18 + a = 18.681541692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + a = 18.681541692 + 18 Combine like terms: -18 + 18 = 0 0 + a = 18.681541692 + 18 a = 18.681541692 + 18 Combine like terms: 18.681541692 + 18 = 36.681541692 a = 36.681541692 Simplifying a = 36.681541692

Subproblem 2

a + -18 = -18.681541692 Simplifying a + -18 = -18.681541692 Reorder the terms: -18 + a = -18.681541692 Solving -18 + a = -18.681541692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + a = -18.681541692 + 18 Combine like terms: -18 + 18 = 0 0 + a = -18.681541692 + 18 a = -18.681541692 + 18 Combine like terms: -18.681541692 + 18 = -0.681541692 a = -0.681541692 Simplifying a = -0.681541692

Solution

The solution to the problem is based on the solutions from the subproblems. a = {36.681541692, -0.681541692}

See similar equations:

| -154=6x-5(6x+2) | | 5x+Solve=8 | | 5400n=180n-360 | | y=-0.5+0.5x | | x^6+6x^4-27x^4=0 | | 3(15x+100)=570 | | 10x+17=3x+-99 | | 548+29.50e=2023 | | n^2+2n-5=3 | | 13.63+0.07(x+3)=14.38-0.15x | | 2880n=180n-360 | | 9w-16.3=55.2 | | 164=-4x+6(-x+9) | | -3x^2-17x-12=-10x-10 | | N+45=172 | | x+2y+4z=12 | | 4(5x-4)=14x+2(3x-8) | | m^2=-13m+42 | | 19-45=4(x-2)-6 | | 1260n=180n-360 | | 1.5x+3=2(x-2.5) | | -8r^2-10=0 | | 2-4m=14 | | X+2y+4z=0 | | 5x-3(x-5)=-9+4x+14 | | 12d+-9=15d+9 | | 7/8m-9=23 | | 23-11a=-43 | | 2+4n=14 | | m^2-77=-4m | | f(x)=5x^2-30x+40 | | 60+45c=285 |

Equations solver categories