d^2+d-8=0

Simple and best practice solution for d^2+d-8=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-8=0 equation: 


Simplifying
d2 + d + -8 = 0

Reorder the terms:
-8 + d + d2 = 0

Solving
-8 + d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + d + 8 + d2 = 0 + 8

Reorder the terms:
-8 + 8 + d + d2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + d + d2 = 0 + 8
d + d2 = 0 + 8

Combine like terms: 0 + 8 = 8
d + d2 = 8

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 = 8 + 0.25

Reorder the terms:
0.25 + d + d2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + d + d2 = 8.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(d + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
d + 0.5 = 2.872281323

Simplifying
d + 0.5 = 2.872281323

Reorder the terms:
0.5 + d = 2.872281323

Solving
0.5 + d = 2.872281323

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 = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = 2.872281323 + -0.5
d = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
d = 2.372281323

Simplifying
d = 2.372281323


Subproblem 2
d + 0.5 = -2.872281323

Simplifying
d + 0.5 = -2.872281323

Reorder the terms:
0.5 + d = -2.872281323

Solving
0.5 + d = -2.872281323

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 = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = -2.872281323 + -0.5
d = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
d = -3.372281323

Simplifying
d = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.372281323, -3.372281323}

See similar equations:

| -2(56x+4)=-3 | | 62w=-2356 | | 3x+6=2(x-8) | | 180=.5x^2+2x+2 | | 9+12x=64x | | 3x+6=2(x-18) | | 10p+6-p=12p-3(p-2) | | 4x-11=3x-14 | | -3(u-v)= | | 3y+2=3y-2 | | 2r+7s-8(6r-2s)= | | 20x^2+11x-4=0 | | 4+5=37 | | 2l+6=bl | | x+x+2=x(x+2)+29 | | 2x^2(x+4)(x+4)=(3x+2)(x-2) | | 3x+6=7x+8 | | 334=2b+14 | | 16x^2-8x+5=0 | | x(x+1)=2*x+1+29 | | 3a+3(a-10)=96 | | 9+x=3-27 | | 5(z-4)-z=4z-20 | | 35-6y=17 | | x^2+20x+9=7x-3 | | 1.8q-4.9-3.1q=-2.3q-3.4 | | 9(v+2)-3v=2(3v+2)-9 | | Rx+sx=1t | | 13(p+8+6q)= | | -1/4(x-8)+1/2(x+2)=x+15 | | 0.1*y=0.09 | | 5a-3+3a=4a+21 |

Equations solver categories