3d^2+d-3=0

Simple and best practice solution for 3d^2+d-3=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 3d^2+d-3=0 equation:


Simplifying
3d2 + d + -3 = 0

Reorder the terms:
-3 + d + 3d2 = 0

Solving
-3 + d + 3d2 = 0

Solving for variable 'd'.

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

Divide each side by '3'.
-1 + 0.3333333333d + d2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333d + d2 = 0 + 1
0.3333333333d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333d + d2 = 1

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.
0.3333333333d + 0.25 + d2 = 1 + 0.25

Reorder the terms:
0.25 + 0.3333333333d + d2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + 0.3333333333d + d2 = 1.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(d + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

d + 0.5 = 1.118033989 Simplifying d + 0.5 = 1.118033989 Reorder the terms: 0.5 + d = 1.118033989 Solving 0.5 + d = 1.118033989 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 = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = 1.118033989 + -0.5 d = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 d = 0.618033989 Simplifying d = 0.618033989

Subproblem 2

d + 0.5 = -1.118033989 Simplifying d + 0.5 = -1.118033989 Reorder the terms: 0.5 + d = -1.118033989 Solving 0.5 + d = -1.118033989 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 = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + d = -1.118033989 + -0.5 d = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 d = -1.618033989 Simplifying d = -1.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.618033989, -1.618033989}

See similar equations:

| 9r^2-24rf+16f^2=0 | | 0.45x+0.5(4-x)=.10(-46) | | b^2+4b-21=0 | | -x-10=-6(4x-6) | | 2x-5=.25x+2 | | x+8=5x-4 | | 25v^2-1=0 | | y=11x-1 | | -2[5+9(8-6)]-8= | | 28k+36(7+k)= | | 4y-8=6y-3y | | abx-d=5d | | 4y-8=6y-3y-4y | | -10(y+8)=-40 | | -10(y+8)=-49 | | 9n+18=18 | | y(x)=2x^3+12x^2+4x | | b^2-77b+12=0 | | -9+7=3x+19 | | 2x+3=.5x | | 8(k-1)=2k-38 | | 4x-x=117 | | 7(3x+2)-5=21x+9 | | 4b^2+6b=1 | | .5x-1=x-4 | | 0.0675= | | 6y^2-13y-3=0 | | -6(t-2)-(t+1)=4 | | 9x^2-54x=0 | | -2x+2=3x+2 | | -9+8(x+6)= | | 6x-2x+9x= |

Equations solver categories