3w^2-1w-45=0

Simple and best practice solution for 3w^2-1w-45=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 3w^2-1w-45=0 equation:


Simplifying
3w2 + -1w + -45 = 0

Reorder the terms:
-45 + -1w + 3w2 = 0

Solving
-45 + -1w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-15 + -0.3333333333w + w2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -0.3333333333w + 15 + w2 = 0 + 15

Reorder the terms:
-15 + 15 + -0.3333333333w + w2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -0.3333333333w + w2 = 0 + 15
-0.3333333333w + w2 = 0 + 15

Combine like terms: 0 + 15 = 15
-0.3333333333w + w2 = 15

The w term is -0.3333333333w.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333w + 0.02777777779 + w2 = 15 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333w + w2 = 15 + 0.02777777779

Combine like terms: 15 + 0.02777777779 = 15.02777777779
0.02777777779 + -0.3333333333w + w2 = 15.02777777779

Factor a perfect square on the left side:
(w + -0.1666666667)(w + -0.1666666667) = 15.02777777779

Calculate the square root of the right side: 3.876567783

Break this problem into two subproblems by setting 
(w + -0.1666666667) equal to 3.876567783 and -3.876567783.

Subproblem 1

w + -0.1666666667 = 3.876567783 Simplifying w + -0.1666666667 = 3.876567783 Reorder the terms: -0.1666666667 + w = 3.876567783 Solving -0.1666666667 + w = 3.876567783 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = 3.876567783 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = 3.876567783 + 0.1666666667 w = 3.876567783 + 0.1666666667 Combine like terms: 3.876567783 + 0.1666666667 = 4.0432344497 w = 4.0432344497 Simplifying w = 4.0432344497

Subproblem 2

w + -0.1666666667 = -3.876567783 Simplifying w + -0.1666666667 = -3.876567783 Reorder the terms: -0.1666666667 + w = -3.876567783 Solving -0.1666666667 + w = -3.876567783 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = -3.876567783 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = -3.876567783 + 0.1666666667 w = -3.876567783 + 0.1666666667 Combine like terms: -3.876567783 + 0.1666666667 = -3.7099011163 w = -3.7099011163 Simplifying w = -3.7099011163

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.0432344497, -3.7099011163}

See similar equations:

| x(3x-8)=48 | | 6-2y+y=4 | | k^2-4k+12=0 | | 25/100=5/x | | 14/42=22/x | | 0.3/24=x/48 | | ln(2x+1)-ln(x-1)=lnx | | 5x=380-42x | | 6a^2+9a-81=0 | | 6x^2-3x+11=0 | | (2x+1)+(3x-4)=12 | | 10x=100y | | 2x-1/34x-5/5 | | 3p-2q=6 | | 25-3t=4(2t-5)-8t | | c-3=6c-48 | | (x+5)(x+15)= | | 2cos^2x-1=1/2 | | 4x^2-23x+27=0 | | 20n+7=12n | | 5x-13=8x+6 | | (X-5)*(x^2+3)=0 | | Ln(x^2+2x-3)=0 | | 6-10y=-4 | | 9-4p=7 | | h=-16x^2+5x+15 | | 1x+1x+3x+3x=232 | | 2(x+4)+2x=12 | | X^2+7y^2-2x-1=0 | | Xsquare-ysquare/100 | | 5/12=3/4*x | | 3G+4=1 |

Equations solver categories