a^2+a=1

Simple and best practice solution for a^2+a=1 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+a=1 equation:


Simplifying
a2 + a = 1

Reorder the terms:
a + a2 = 1

Solving
a + a2 = 1

Solving for variable 'a'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = 1 + 0.25

Reorder the terms:
0.25 + a + a2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + a + a2 = 1.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(a + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

a + 0.5 = 1.118033989 Simplifying a + 0.5 = 1.118033989 Reorder the terms: 0.5 + a = 1.118033989 Solving 0.5 + a = 1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.118033989 + -0.5 a = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 a = 0.618033989 Simplifying a = 0.618033989

Subproblem 2

a + 0.5 = -1.118033989 Simplifying a + 0.5 = -1.118033989 Reorder the terms: 0.5 + a = -1.118033989 Solving 0.5 + a = -1.118033989 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.118033989 + -0.5 a = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 a = -1.618033989 Simplifying a = -1.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.618033989, -1.618033989}

See similar equations:

| K-6.4=2.9 | | 448=-8(-10x+4) | | 4x+3(-5x-3)=-64 | | 7(5y-1)=28y | | 20=2+8k+k | | -3+5x-7=20 | | 90=(4x+3) | | 12+2z=5z+27 | | 5x-125=55 | | I-38=46 | | y=625+144 | | 36(x-2)= | | 85-x=10 | | 23-(7t-7)=45t-4 | | 5(2x-1)+2=7(x+3) | | J-647=353 | | -3x+6-2x=7x+8 | | -36+s=31 | | -396=-9(8x-12) | | 6(2x-4)=3(4x-22) | | 4a+3=-9 | | p^2-10p-15=0 | | 3t-18=4t-16 | | 6x-2=70 | | -498=6(9x+16) | | 20=-3x+7(-2x+25) | | -7(x+8)-44=3-61 | | 8x^3-336x^2+2760x+1608= | | 2(7-3x)+1=2x-1 | | (3x+4)(x-3)=10 | | 8+-176=-72 | | 567=-6(10x-16) |

Equations solver categories