-16a^2-5a+312=0

Simple and best practice solution for -16a^2-5a+312=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 -16a^2-5a+312=0 equation:


Simplifying
-16a2 + -5a + 312 = 0

Reorder the terms:
312 + -5a + -16a2 = 0

Solving
312 + -5a + -16a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-19.5 + 0.3125a + a2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + 0.3125a + 19.5 + a2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + 0.3125a + a2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + 0.3125a + a2 = 0 + 19.5
0.3125a + a2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
0.3125a + a2 = 19.5

The a term is 0.3125a.  Take half its coefficient (0.15625).
Square it (0.0244140625) and add it to both sides.

Add '0.0244140625' to each side of the equation.
0.3125a + 0.0244140625 + a2 = 19.5 + 0.0244140625

Reorder the terms:
0.0244140625 + 0.3125a + a2 = 19.5 + 0.0244140625

Combine like terms: 19.5 + 0.0244140625 = 19.5244140625
0.0244140625 + 0.3125a + a2 = 19.5244140625

Factor a perfect square on the left side:
(a + 0.15625)(a + 0.15625) = 19.5244140625

Calculate the square root of the right side: 4.418643917

Break this problem into two subproblems by setting 
(a + 0.15625) equal to 4.418643917 and -4.418643917.

Subproblem 1

a + 0.15625 = 4.418643917 Simplifying a + 0.15625 = 4.418643917 Reorder the terms: 0.15625 + a = 4.418643917 Solving 0.15625 + a = 4.418643917 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + a = 4.418643917 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + a = 4.418643917 + -0.15625 a = 4.418643917 + -0.15625 Combine like terms: 4.418643917 + -0.15625 = 4.262393917 a = 4.262393917 Simplifying a = 4.262393917

Subproblem 2

a + 0.15625 = -4.418643917 Simplifying a + 0.15625 = -4.418643917 Reorder the terms: 0.15625 + a = -4.418643917 Solving 0.15625 + a = -4.418643917 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + a = -4.418643917 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + a = -4.418643917 + -0.15625 a = -4.418643917 + -0.15625 Combine like terms: -4.418643917 + -0.15625 = -4.574893917 a = -4.574893917 Simplifying a = -4.574893917

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.262393917, -4.574893917}

See similar equations:

| 3n-6+2n=-7+4n | | 25p-4=71p-96 | | x+(-3)=11 | | X^2+6=8x-3 | | 6=4c+9y | | x^2+14x=0.009 | | x^2+14x=0.004 | | 4(n-7)-2(n+3)=15n | | 9y+9=21 | | 4x+32=-12 | | R-23=6 | | 8w-2w=6 | | 5z-4.8=5.7z-7.88 | | -8g+5+2g=9-6g-4 | | -24=-53 | | 2y^2-12x-7=0 | | 2y+3y=12y | | O=-3y-10+4y | | 39a+4-20a=42 | | 15x^2-8x-16= | | 27=7-2y | | x^3+2x^2-83=0 | | 12a+2-10a=14 | | 2(3n-4)=8b-11 | | 5b+2-b=86 | | 7x-32=-3 | | 2c^3+4c^2-30c=0 | | x^3+2x^2-23-60=0 | | 2x^2+25-32=0 | | 105x^8-175x^7+84x^6-140x^5=0 | | X^2-55x-60=0 | | 6x+5=-4x-15 |

Equations solver categories