4x^2+4x+1=500000

Simple and best practice solution for 4x^2+4x+1=500000 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 4x^2+4x+1=500000 equation:


Simplifying
4x2 + 4x + 1 = 500000

Reorder the terms:
1 + 4x + 4x2 = 500000

Solving
1 + 4x + 4x2 = 500000

Solving for variable 'x'.

Reorder the terms:
1 + -500000 + 4x + 4x2 = 500000 + -500000

Combine like terms: 1 + -500000 = -499999
-499999 + 4x + 4x2 = 500000 + -500000

Combine like terms: 500000 + -500000 = 0
-499999 + 4x + 4x2 = 0

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

Divide each side by '4'.
-124999.75 + x + x2 = 0

Move the constant term to the right:

Add '124999.75' to each side of the equation.
-124999.75 + x + 124999.75 + x2 = 0 + 124999.75

Reorder the terms:
-124999.75 + 124999.75 + x + x2 = 0 + 124999.75

Combine like terms: -124999.75 + 124999.75 = 0.00
0.00 + x + x2 = 0 + 124999.75
x + x2 = 0 + 124999.75

Combine like terms: 0 + 124999.75 = 124999.75
x + x2 = 124999.75

The x term is x.  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.
 + 0.25 + x2 = 124999.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 124999.75 + 0.25

Combine like terms: 124999.75 + 0.25 = 125000
1.25 + x2 = 125000

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 125000

Calculate the square root of the right side: 353.553390593

Break this problem into two subproblems by setting 
(x + 0.5) equal to 353.553390593 and -353.553390593.

Subproblem 1

x + 0.5 = 353.553390593 Simplifying x + 0.5 = 353.553390593 Reorder the terms: 0.5 + x = 353.553390593 Solving 0.5 + x = 353.553390593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 353.553390593 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 353.553390593 + -0.5 x = 353.553390593 + -0.5 Combine like terms: 353.553390593 + -0.5 = 353.053390593 x = 353.053390593 Simplifying x = 353.053390593

Subproblem 2

x + 0.5 = -353.553390593 Simplifying x + 0.5 = -353.553390593 Reorder the terms: 0.5 + x = -353.553390593 Solving 0.5 + x = -353.553390593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -353.553390593 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -353.553390593 + -0.5 x = -353.553390593 + -0.5 Combine like terms: -353.553390593 + -0.5 = -354.053390593 x = -354.053390593 Simplifying x = -354.053390593

Solution

The solution to the problem is based on the solutions from the subproblems. x = {353.053390593, -354.053390593}

See similar equations:

| -9+6x=-9 | | 2k-3k=-8(7k-1)-8(1+7k) | | 1+5^2/50 | | 4y+2y*2=21 | | (5-3x)/(2x^2-14x+20) | | 1/2a+3=11 | | 11+3x/6 | | 4(3x-1)-1(x+5)=24 | | -9-6x+2.5=-8x+3.7 | | r/3+7=12 | | 2/3=(4*f)/6 | | (28b-4)-9(3b+4)=-5 | | 0.2x+0.6-8x+12=0.9 | | (x^3-15x^2-50x)/(3x^3+8x^2-16x)=0 | | c=48y+0.99 | | 6p+24=4p-3+1 | | A=r/22 | | 2x-14=70 | | x^3-5x^2-50x=0 | | 9x+11=4x-24 | | x+.051675x=1058 | | 4y+3y^2=21 | | 2(5x-7)=6(5x+9)+28 | | 300=u-144 | | 10x+8-7x=-7 | | -40=-13m-7m | | 50(2w-4)=-10 | | 6(5k+6)+5k=-4k-3 | | 60=(x+5)(y-2) | | -18+3x=-3 | | 24=-22+2x | | 4x+1=6x+13 |

Equations solver categories