a^2+2a-31=0

Simple and best practice solution for a^2+2a-31=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 a^2+2a-31=0 equation:


Simplifying
a2 + 2a + -31 = 0

Reorder the terms:
-31 + 2a + a2 = 0

Solving
-31 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2a + 31 + a2 = 0 + 31

Reorder the terms:
-31 + 31 + 2a + a2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2a + a2 = 0 + 31
2a + a2 = 0 + 31

Combine like terms: 0 + 31 = 31
2a + a2 = 31

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 31 + 1

Reorder the terms:
1 + 2a + a2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + 2a + a2 = 32

Factor a perfect square on the left side:
(a + 1)(a + 1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(a + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1

a + 1 = 5.656854249 Simplifying a + 1 = 5.656854249 Reorder the terms: 1 + a = 5.656854249 Solving 1 + a = 5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.656854249 + -1 a = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 a = 4.656854249 Simplifying a = 4.656854249

Subproblem 2

a + 1 = -5.656854249 Simplifying a + 1 = -5.656854249 Reorder the terms: 1 + a = -5.656854249 Solving 1 + a = -5.656854249 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.656854249 + -1 a = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 a = -6.656854249 Simplifying a = -6.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.656854249, -6.656854249}

See similar equations:

| 15y-9y^2= | | 4b^2-20b+5=0 | | b^2-12b+32= | | (x-2)/4=(x+4)/2 | | 40-(1/4)Q | | 14.4/12 | | (3x-5)/4=-5/7 | | -7(7b+5)-3b=175 | | 2x^2-12x-63=0 | | x+2(1-x)=10-3x | | 5b-10=25 | | n^2-21n+20= | | 3G-12=-3 | | y^3-5y=0 | | -11+3/2 | | (x+2)/3=8/9 | | 12-x/3=7 | | (7/2)x-(1-x/2)=4 | | Log(1-x)=3 | | 3/4x+4=10 | | An=3n+4n | | 3a+(4b+3)i=9-6i | | 9x^2-72xy+21x-84y+144y^2-8=0 | | x-39=-44 | | 4.6-8.8=7 | | 2y+4-9=16 | | -m/6+6=41 | | (-2)+x=-31 | | An=7n+11 | | 12-2(x^2-2x*1+1)=4(x-2)-(x-3)(2x-5) | | 17.5=7w | | (-11)+x=-28 |

Equations solver categories