d^2+d-400=0

Simple and best practice solution for d^2+d-400=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 d^2+d-400=0 equation:


Simplifying
d2 + d + -400 = 0

Reorder the terms:
-400 + d + d2 = 0

Solving
-400 + d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + d + 400 + d2 = 0 + 400

Reorder the terms:
-400 + 400 + d + d2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + d + d2 = 0 + 400
d + d2 = 0 + 400

Combine like terms: 0 + 400 = 400
d + d2 = 400

The d term is d.  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.
d + 0.25 + d2 = 400 + 0.25

Reorder the terms:
0.25 + d + d2 = 400 + 0.25

Combine like terms: 400 + 0.25 = 400.25
0.25 + d + d2 = 400.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(d + 0.5) equal to 20.006249024 and -20.006249024.

Subproblem 1

d + 0.5 = 20.006249024 Simplifying d + 0.5 = 20.006249024 Reorder the terms: 0.5 + d = 20.006249024 Solving 0.5 + d = 20.006249024 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = 20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = 20.006249024 + -0.5 d = 20.006249024 + -0.5 Combine like terms: 20.006249024 + -0.5 = 19.506249024 d = 19.506249024 Simplifying d = 19.506249024

Subproblem 2

d + 0.5 = -20.006249024 Simplifying d + 0.5 = -20.006249024 Reorder the terms: 0.5 + d = -20.006249024 Solving 0.5 + d = -20.006249024 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + d = -20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = -20.006249024 + -0.5 d = -20.006249024 + -0.5 Combine like terms: -20.006249024 + -0.5 = -20.506249024 d = -20.506249024 Simplifying d = -20.506249024

Solution

The solution to the problem is based on the solutions from the subproblems. d = {19.506249024, -20.506249024}

See similar equations:

| -2x+3=19+6x | | 5m=0.95 | | u^5-13u^2+36=0 | | 8(8)-11= | | 4-x+7+5x= | | -2x-5-2(x-3)=9x-(7x-8)-8x+5 | | -6(10+8)+9(5r+8)= | | -39-35= | | 5.5t=22 | | 4x+9=47 | | 3y-4/5y=22 | | -8-5f=12-9f | | 65+(4x-1)=180 | | 19-2n=-9 | | 2(x-10)+4x=-6x+2 | | n/8=28/32 | | 3y-4y=22 | | 8f=36 | | -18w-3+3w-12= | | -2x-5-2(x-3)=2x-(7x-8)-8x+5 | | -3(-3)+4(-4)= | | -3(-7)+4(-7)= | | 6*6n=96 | | y=4sin(x+pi) | | 46774x-86=64774+67x | | 748=x*880 | | 2x+14+x+20=180 | | -3(-9)+4(2)= | | f-4=9 | | -3(-9)+4(2)y= | | x+y=77 | | 15x+20(((3x+1)3)-5)=875 |

Equations solver categories