2a^2+a=186

Simple and best practice solution for 2a^2+a=186 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 2a^2+a=186 equation:


Simplifying
2a2 + a = 186

Reorder the terms:
a + 2a2 = 186

Solving
a + 2a2 = 186

Solving for variable 'a'.

Reorder the terms:
-186 + a + 2a2 = 186 + -186

Combine like terms: 186 + -186 = 0
-186 + a + 2a2 = 0

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

Divide each side by '2'.
-93 + 0.5a + a2 = 0

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 0.5a + 93 + a2 = 0 + 93

Reorder the terms:
-93 + 93 + 0.5a + a2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 0.5a + a2 = 0 + 93
0.5a + a2 = 0 + 93

Combine like terms: 0 + 93 = 93
0.5a + a2 = 93

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.
0.5a + 0.25 + a2 = 93 + 0.25

Reorder the terms:
0.25 + 0.5a + a2 = 93 + 0.25

Combine like terms: 93 + 0.25 = 93.25
0.25 + 0.5a + a2 = 93.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 93.25

Calculate the square root of the right side: 9.656603958

Break this problem into two subproblems by setting 
(a + 0.5) equal to 9.656603958 and -9.656603958.

Subproblem 1

a + 0.5 = 9.656603958 Simplifying a + 0.5 = 9.656603958 Reorder the terms: 0.5 + a = 9.656603958 Solving 0.5 + a = 9.656603958 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 = 9.656603958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 9.656603958 + -0.5 a = 9.656603958 + -0.5 Combine like terms: 9.656603958 + -0.5 = 9.156603958 a = 9.156603958 Simplifying a = 9.156603958

Subproblem 2

a + 0.5 = -9.656603958 Simplifying a + 0.5 = -9.656603958 Reorder the terms: 0.5 + a = -9.656603958 Solving 0.5 + a = -9.656603958 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 = -9.656603958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -9.656603958 + -0.5 a = -9.656603958 + -0.5 Combine like terms: -9.656603958 + -0.5 = -10.156603958 a = -10.156603958 Simplifying a = -10.156603958

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.156603958, -10.156603958}

See similar equations:

| 2/7p=-6/5 | | -12-3y=12 | | 5x+12=2(2x+8) | | -2/2= | | 90/5x-7 | | -7n-5=-145 | | 1/2(x+2)=-5 | | 9y+7=5y-5 | | 4n+20=50-2n | | 41-x=20+2x | | 8-3x=3x^2 | | 4g-(2+g)=10+2g | | 3/4(6g-2)+7=19 | | x(x-2)-13=0 | | 5(3x-2b)=2x-b | | 5(v+8)=10 | | (2x-y)+(x+4y)=180 | | 14=15z-2z+12 | | 1/5+3/2x=3/4 | | 14=15z-2z+14 | | 6x^2-15x+11=0 | | 9x^2-9=5 | | 14(3-7x)=-(3+2x) | | y-6=-3/5x | | -1/3a-1/2a | | 2(16/3+3)+2(16/3*2-6) | | 2x-14-12=-12 | | (14m+4)-(5m-6)= | | -1/3-1/2 | | 180-3y+3y=180 | | x^2+9z+20=0 | | 3x-9x+16=2x+1 |

Equations solver categories