7a^2+32a=7-40a

Simple and best practice solution for 7a^2+32a=7-40a 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 7a^2+32a=7-40a equation:


Simplifying
7a2 + 32a = 7 + -40a

Reorder the terms:
32a + 7a2 = 7 + -40a

Solving
32a + 7a2 = 7 + -40a

Solving for variable 'a'.

Reorder the terms:
-7 + 32a + 40a + 7a2 = 7 + -40a + -7 + 40a

Combine like terms: 32a + 40a = 72a
-7 + 72a + 7a2 = 7 + -40a + -7 + 40a

Reorder the terms:
-7 + 72a + 7a2 = 7 + -7 + -40a + 40a

Combine like terms: 7 + -7 = 0
-7 + 72a + 7a2 = 0 + -40a + 40a
-7 + 72a + 7a2 = -40a + 40a

Combine like terms: -40a + 40a = 0
-7 + 72a + 7a2 = 0

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

Divide each side by '7'.
-1 + 10.28571429a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 10.28571429a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 10.28571429a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10.28571429a + a2 = 0 + 1
10.28571429a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
10.28571429a + a2 = 1

The a term is 10.28571429a.  Take half its coefficient (5.142857145).
Square it (26.44897961) and add it to both sides.

Add '26.44897961' to each side of the equation.
10.28571429a + 26.44897961 + a2 = 1 + 26.44897961

Reorder the terms:
26.44897961 + 10.28571429a + a2 = 1 + 26.44897961

Combine like terms: 1 + 26.44897961 = 27.44897961
26.44897961 + 10.28571429a + a2 = 27.44897961

Factor a perfect square on the left side:
(a + 5.142857145)(a + 5.142857145) = 27.44897961

Calculate the square root of the right side: 5.239177379

Break this problem into two subproblems by setting 
(a + 5.142857145) equal to 5.239177379 and -5.239177379.

Subproblem 1

a + 5.142857145 = 5.239177379 Simplifying a + 5.142857145 = 5.239177379 Reorder the terms: 5.142857145 + a = 5.239177379 Solving 5.142857145 + a = 5.239177379 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.142857145' to each side of the equation. 5.142857145 + -5.142857145 + a = 5.239177379 + -5.142857145 Combine like terms: 5.142857145 + -5.142857145 = 0.000000000 0.000000000 + a = 5.239177379 + -5.142857145 a = 5.239177379 + -5.142857145 Combine like terms: 5.239177379 + -5.142857145 = 0.096320234 a = 0.096320234 Simplifying a = 0.096320234

Subproblem 2

a + 5.142857145 = -5.239177379 Simplifying a + 5.142857145 = -5.239177379 Reorder the terms: 5.142857145 + a = -5.239177379 Solving 5.142857145 + a = -5.239177379 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.142857145' to each side of the equation. 5.142857145 + -5.142857145 + a = -5.239177379 + -5.142857145 Combine like terms: 5.142857145 + -5.142857145 = 0.000000000 0.000000000 + a = -5.239177379 + -5.142857145 a = -5.239177379 + -5.142857145 Combine like terms: -5.239177379 + -5.142857145 = -10.382034524 a = -10.382034524 Simplifying a = -10.382034524

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.096320234, -10.382034524}

See similar equations:

| 5w+3=3+2w | | c=x+0.06x+0.15y | | 36-9-8b=11 | | -5=-x-(-17) | | 5+2(x+4)=2x+4+3x | | 7(-1-v)=-7v-3 | | 6x+12=5x+40 | | 2h-3=11 | | 6x+8+-4x=4(x+2) | | -5=5x-(-17) | | 2y+5x=270 | | 12-(3x+7)=8 | | 3(t-3)=27 | | 3x^6+22x^3+35=0 | | 0.3(-12x)=-24 | | (3x^6+9x^8-3+7x^7)-(6+9x^7+5x^8+9x^6)= | | 6x+55=16x-75 | | 200m-125+43650=45225-150m | | x-(3x-12)=-8 | | -32+x=7x+58 | | 12x+36= | | 2(3+4x)=y | | 3x+5-(2x+9)=-(5x-2) | | 3y=y+1+3 | | 3n-7=4+2n | | -5(8v+8)=8(-5v-5) | | 4=3a-(-4) | | 50x-20=60 | | 10+7x=75 | | 5a-30b= | | (2*3.5-10)=x | | (y+2)(y-4)=3x |

Equations solver categories