(4w+10)*w=103

Simple and best practice solution for (4w+10)*w=103 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+10)*w=103 equation:


Simplifying
(4w + 10) * w = 103

Reorder the terms:
(10 + 4w) * w = 103

Reorder the terms for easier multiplication:
w(10 + 4w) = 103
(10 * w + 4w * w) = 103
(10w + 4w2) = 103

Solving
10w + 4w2 = 103

Solving for variable 'w'.

Reorder the terms:
-103 + 10w + 4w2 = 103 + -103

Combine like terms: 103 + -103 = 0
-103 + 10w + 4w2 = 0

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

Divide each side by '4'.
-25.75 + 2.5w + w2 = 0

Move the constant term to the right:

Add '25.75' to each side of the equation.
-25.75 + 2.5w + 25.75 + w2 = 0 + 25.75

Reorder the terms:
-25.75 + 25.75 + 2.5w + w2 = 0 + 25.75

Combine like terms: -25.75 + 25.75 = 0.00
0.00 + 2.5w + w2 = 0 + 25.75
2.5w + w2 = 0 + 25.75

Combine like terms: 0 + 25.75 = 25.75
2.5w + w2 = 25.75

The w term is 2.5w.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5w + 1.5625 + w2 = 25.75 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 25.75 + 1.5625

Combine like terms: 25.75 + 1.5625 = 27.3125
1.5625 + 2.5w + w2 = 27.3125

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 27.3125

Calculate the square root of the right side: 5.22613624

Break this problem into two subproblems by setting 
(w + 1.25) equal to 5.22613624 and -5.22613624.

Subproblem 1

w + 1.25 = 5.22613624 Simplifying w + 1.25 = 5.22613624 Reorder the terms: 1.25 + w = 5.22613624 Solving 1.25 + w = 5.22613624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 5.22613624 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 5.22613624 + -1.25 w = 5.22613624 + -1.25 Combine like terms: 5.22613624 + -1.25 = 3.97613624 w = 3.97613624 Simplifying w = 3.97613624

Subproblem 2

w + 1.25 = -5.22613624 Simplifying w + 1.25 = -5.22613624 Reorder the terms: 1.25 + w = -5.22613624 Solving 1.25 + w = -5.22613624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -5.22613624 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -5.22613624 + -1.25 w = -5.22613624 + -1.25 Combine like terms: -5.22613624 + -1.25 = -6.47613624 w = -6.47613624 Simplifying w = -6.47613624

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.97613624, -6.47613624}

See similar equations:

| (8y-7)-(8y-7)= | | 2(5m-9)-16= | | -8(x+5)+6=-34 | | 9w+7=7w+31 | | (7g+2)-(5g+1)= | | 89x+68+23=180 | | -3j^2*k^-4/-9j^-2k | | 7xy+6y= | | 1/3(5x−7) | | -3j^2k^-4/-9j^-2k | | 15x+15=10x+40 | | -1/3(18x-15y)= | | 89x+68+23=18 | | 2a+3p=.82 | | 2t^3(t^2+t-64)=0 | | 3-x+7=12 | | 3a+2p=.78 | | (x^4/3)=81 | | 29=-14n+1 | | x^2+4xy+4y=1 | | 8p+6=7p+10 | | 44d=33333334556789001245 | | (d-3).40=30 | | -4=-24x | | 0.555555556(8+c)=-20 | | 66y=10084 | | 41=17+2g-100 | | 3+0.1n+0.7n=7.8 | | x^2+2y^2=81 | | 5ln(x)=-1 | | 3(x-1)=2(3x-9) | | 1000/0 |

Equations solver categories