4w^2-31w+15=0

Simple and best practice solution for 4w^2-31w+15=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 4w^2-31w+15=0 equation:


Simplifying
4w2 + -31w + 15 = 0

Reorder the terms:
15 + -31w + 4w2 = 0

Solving
15 + -31w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
3.75 + -7.75w + w2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -7.75w + -3.75 + w2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -7.75w + w2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -7.75w + w2 = 0 + -3.75
-7.75w + w2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-7.75w + w2 = -3.75

The w term is -7.75w.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75w + 15.015625 + w2 = -3.75 + 15.015625

Reorder the terms:
15.015625 + -7.75w + w2 = -3.75 + 15.015625

Combine like terms: -3.75 + 15.015625 = 11.265625
15.015625 + -7.75w + w2 = 11.265625

Factor a perfect square on the left side:
(w + -3.875)(w + -3.875) = 11.265625

Calculate the square root of the right side: 3.356430396

Break this problem into two subproblems by setting 
(w + -3.875) equal to 3.356430396 and -3.356430396.

Subproblem 1

w + -3.875 = 3.356430396 Simplifying w + -3.875 = 3.356430396 Reorder the terms: -3.875 + w = 3.356430396 Solving -3.875 + w = 3.356430396 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + w = 3.356430396 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + w = 3.356430396 + 3.875 w = 3.356430396 + 3.875 Combine like terms: 3.356430396 + 3.875 = 7.231430396 w = 7.231430396 Simplifying w = 7.231430396

Subproblem 2

w + -3.875 = -3.356430396 Simplifying w + -3.875 = -3.356430396 Reorder the terms: -3.875 + w = -3.356430396 Solving -3.875 + w = -3.356430396 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + w = -3.356430396 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + w = -3.356430396 + 3.875 w = -3.356430396 + 3.875 Combine like terms: -3.356430396 + 3.875 = 0.518569604 w = 0.518569604 Simplifying w = 0.518569604

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.231430396, 0.518569604}

See similar equations:

| 2(3x+1)=9x+(3-3x) | | 4w^2-31w+12=0 | | x+8=-4x+2 | | 7-4[9-(7y-7)]= | | 12+x+x=180 | | (6+y)(4y-9)=0 | | F(x)=2x+2x-x | | 10-3/4x=10 | | 6w^1+11w+3=0 | | (6m^4-2m^2+m)-(4m^3+4m^2+7m)+(m^2-m)= | | 9x+1=323666113 | | 5n^2+27n-49=7 | | 6X+1=313914040 | | y-3=9(x+10) | | -10+7x=-59 | | 6X+1=9752073 | | 3x=87-6 | | 36x/6x^3 | | 5u^2-4u-12=0 | | y-3=9(x/10) | | 7(x-1)/5=x-9 | | 5x+(19x+12)+(27x-3)=180 | | 2x+1=5x+1-3x | | -(8-T)+(2T-6)= | | Z-18=20 | | x+1=(9x^2)+6x+1 | | x+x+x-3=180 | | 22r=22 | | log(x+6)-log(2x-1)=1 | | 42=x+10 | | x+(x+1)+(x+3)=21 | | 23x-19y=7 |

Equations solver categories