2w^2+21w+52=69

Simple and best practice solution for 2w^2+21w+52=69 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 2w^2+21w+52=69 equation:


Simplifying
2w2 + 21w + 52 = 69

Reorder the terms:
52 + 21w + 2w2 = 69

Solving
52 + 21w + 2w2 = 69

Solving for variable 'w'.

Reorder the terms:
52 + -69 + 21w + 2w2 = 69 + -69

Combine like terms: 52 + -69 = -17
-17 + 21w + 2w2 = 69 + -69

Combine like terms: 69 + -69 = 0
-17 + 21w + 2w2 = 0

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

Divide each side by '2'.
-8.5 + 10.5w + w2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 10.5w + 8.5 + w2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 10.5w + w2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 10.5w + w2 = 0 + 8.5
10.5w + w2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
10.5w + w2 = 8.5

The w term is 10.5w.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5w + 27.5625 + w2 = 8.5 + 27.5625

Reorder the terms:
27.5625 + 10.5w + w2 = 8.5 + 27.5625

Combine like terms: 8.5 + 27.5625 = 36.0625
27.5625 + 10.5w + w2 = 36.0625

Factor a perfect square on the left side:
(w + 5.25)(w + 5.25) = 36.0625

Calculate the square root of the right side: 6.005206075

Break this problem into two subproblems by setting 
(w + 5.25) equal to 6.005206075 and -6.005206075.

Subproblem 1

w + 5.25 = 6.005206075 Simplifying w + 5.25 = 6.005206075 Reorder the terms: 5.25 + w = 6.005206075 Solving 5.25 + w = 6.005206075 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + w = 6.005206075 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + w = 6.005206075 + -5.25 w = 6.005206075 + -5.25 Combine like terms: 6.005206075 + -5.25 = 0.755206075 w = 0.755206075 Simplifying w = 0.755206075

Subproblem 2

w + 5.25 = -6.005206075 Simplifying w + 5.25 = -6.005206075 Reorder the terms: 5.25 + w = -6.005206075 Solving 5.25 + w = -6.005206075 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + w = -6.005206075 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + w = -6.005206075 + -5.25 w = -6.005206075 + -5.25 Combine like terms: -6.005206075 + -5.25 = -11.255206075 w = -11.255206075 Simplifying w = -11.255206075

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.755206075, -11.255206075}

See similar equations:

| 9y-8b=13.83 | | 26-2t=-12 | | 5+0.8=14.6 | | 4y-10x=-8 | | 0.0476x^2-0.1=0 | | 3x-4x+20=24 | | 8(5x-5)-4=2(6-8x) | | 6.99-0.55=11.95 | | -q=21 | | y=4x^2-13 | | 2x+10=x+26 | | 84h-65h-15h+4=56 | | 4(2x-7)=16 | | 27+4w=5w | | 67-x=76-2x | | 7n-6=-146 | | -88=2(g+42) | | 6x^19=0 | | 8=67-k | | 4y-4x=-8 | | 6=20(0.9)x | | x^2-80x-500=0 | | 6x+y=78 | | 3x-42=2x+9 | | x^2-80x-5000=0 | | 92.7=9(m+2.1) | | 3x=13.5 | | 5x-7+3x+17=180 | | 6-2(x-5)=x-3 | | 64F-1=30F-6 | | 6(r+-11)-29=-11 | | F^2-22f+9=0 |

Equations solver categories