w^2+2w=72

Simple and best practice solution for w^2+2w=72 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 w^2+2w=72 equation:


Simplifying
w2 + 2w = 72

Reorder the terms:
2w + w2 = 72

Solving
2w + w2 = 72

Solving for variable 'w'.

Reorder the terms:
-72 + 2w + w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 2w + 72 + w2 = 0 + 72

Reorder the terms:
-72 + 72 + 2w + w2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 2w + w2 = 0 + 72
2w + w2 = 0 + 72

Combine like terms: 0 + 72 = 72
2w + w2 = 72

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 72 + 1

Reorder the terms:
1 + 2w + w2 = 72 + 1

Combine like terms: 72 + 1 = 73
1 + 2w + w2 = 73

Factor a perfect square on the left side:
(w + 1)(w + 1) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(w + 1) equal to 8.544003745 and -8.544003745.

Subproblem 1

w + 1 = 8.544003745 Simplifying w + 1 = 8.544003745 Reorder the terms: 1 + w = 8.544003745 Solving 1 + w = 8.544003745 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + w = 8.544003745 + -1 w = 8.544003745 + -1 Combine like terms: 8.544003745 + -1 = 7.544003745 w = 7.544003745 Simplifying w = 7.544003745

Subproblem 2

w + 1 = -8.544003745 Simplifying w + 1 = -8.544003745 Reorder the terms: 1 + w = -8.544003745 Solving 1 + w = -8.544003745 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -8.544003745 + -1 Combine like terms: 1 + -1 = 0 0 + w = -8.544003745 + -1 w = -8.544003745 + -1 Combine like terms: -8.544003745 + -1 = -9.544003745 w = -9.544003745 Simplifying w = -9.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.544003745, -9.544003745}

See similar equations:

| Q=100-p | | 4(4+x)+33x=15x | | 8x+y=120 | | (2/3)^-4 | | -3(3s-4)-12=-2(8s+5)-2 | | 2/3/100*5=4/7/100x | | (2x+3)(5x-9)/(5x-9)(4x-7) | | 13x^2+4x-9=0 | | 8+12z-24=-4z+12+6 | | f(x)=6x^2+9x+7 | | (2x-1)/(x+9)=5/4 | | (x)=5x^2+7x+2 | | 5x+10(200-x)=45x | | 5x+10(200-x)=45 | | fx=5x^2+7x+2 | | 16a+17b=100 | | 16a+17b+23c=100 | | y-5=6/5(x-2) | | 16a+17b+23c+24d+39e+40f=100 | | .02(60)+.04x=.03(50+x) | | f(x)=5x^2+7x+2 | | 15x+10-7x+28=60 | | (-5x-5y)-(2x-8y)= | | (y+5)(y+6)=0 | | 2c^3+14c^2-36=0 | | 6-30-3x=5x | | x+7+6x-24=-24 | | 8*-9/-3*2/5 | | w/6.5=9.4 | | z/7.3=4 | | 2z^2(4z^2-9z-9)= | | 0.40c+(0.75)(500-c)= |

Equations solver categories