4a^2+16a-1=2

Simple and best practice solution for 4a^2+16a-1=2 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 4a^2+16a-1=2 equation:


Simplifying
4a2 + 16a + -1 = 2

Reorder the terms:
-1 + 16a + 4a2 = 2

Solving
-1 + 16a + 4a2 = 2

Solving for variable 'a'.

Reorder the terms:
-1 + -2 + 16a + 4a2 = 2 + -2

Combine like terms: -1 + -2 = -3
-3 + 16a + 4a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-3 + 16a + 4a2 = 0

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

Divide each side by '4'.
-0.75 + 4a + a2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 4a + 0.75 + a2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 4a + a2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 4a + a2 = 0 + 0.75
4a + a2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
4a + a2 = 0.75

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 0.75 + 4

Reorder the terms:
4 + 4a + a2 = 0.75 + 4

Combine like terms: 0.75 + 4 = 4.75
4 + 4a + a2 = 4.75

Factor a perfect square on the left side:
(a + 2)(a + 2) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(a + 2) equal to 2.179449472 and -2.179449472.

Subproblem 1

a + 2 = 2.179449472 Simplifying a + 2 = 2.179449472 Reorder the terms: 2 + a = 2.179449472 Solving 2 + a = 2.179449472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.179449472 + -2 a = 2.179449472 + -2 Combine like terms: 2.179449472 + -2 = 0.179449472 a = 0.179449472 Simplifying a = 0.179449472

Subproblem 2

a + 2 = -2.179449472 Simplifying a + 2 = -2.179449472 Reorder the terms: 2 + a = -2.179449472 Solving 2 + a = -2.179449472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.179449472 + -2 a = -2.179449472 + -2 Combine like terms: -2.179449472 + -2 = -4.179449472 a = -4.179449472 Simplifying a = -4.179449472

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.179449472, -4.179449472}

See similar equations:

| 38(r+8)=9 | | 3m-20=130 | | X^4+16x^2-48=0 | | 10p^2+20p-38=-8 | | -3-3y=15 | | 7(2l+4)=126 | | 8k^2-16k-6=4 | | 13=n-(-3) | | 6i-19=29 | | 5x-3*2x-9*3x-2=7106 | | 2(a-1)=44 | | 5sin(x)-7cos(x)=0 | | (2x-3)(4x+9)= | | 8=1 | | x+4=80 | | 3+7x=9.4+3x | | 3x^2+5x+12=-10 | | 12y+2=42 | | 2(3x+1)=26-2x | | ln(211)=x | | 2x+(x*x)=3 | | 2.5x+14+3.5x=-4x-26 | | 15b^2-24bf=0 | | 20f+44=63 | | 6x+37=-16x-73 | | dx(x+1)=ydx | | 4x+7=2x-12 | | dt(x+1)=ydx | | 5(7-x)(2x+8)=0 | | 20x+20=25x+10 | | 2023mb=s*12138 | | 5cos^2x-7cos+2=0 |

Equations solver categories