(2w-17.5)(w-2.5)=10.5

Simple and best practice solution for (2w-17.5)(w-2.5)=10.5 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-17.5)(w-2.5)=10.5 equation:


Simplifying
(2w + -17.5)(w + -2.5) = 10.5

Reorder the terms:
(-17.5 + 2w)(w + -2.5) = 10.5

Reorder the terms:
(-17.5 + 2w)(-2.5 + w) = 10.5

Multiply (-17.5 + 2w) * (-2.5 + w)
(-17.5(-2.5 + w) + 2w * (-2.5 + w)) = 10.5
((-2.5 * -17.5 + w * -17.5) + 2w * (-2.5 + w)) = 10.5
((43.75 + -17.5w) + 2w * (-2.5 + w)) = 10.5
(43.75 + -17.5w + (-2.5 * 2w + w * 2w)) = 10.5
(43.75 + -17.5w + (-5w + 2w2)) = 10.5

Combine like terms: -17.5w + -5w = -22.5w
(43.75 + -22.5w + 2w2) = 10.5

Solving
43.75 + -22.5w + 2w2 = 10.5

Solving for variable 'w'.

Reorder the terms:
43.75 + -10.5 + -22.5w + 2w2 = 10.5 + -10.5

Combine like terms: 43.75 + -10.5 = 33.25
33.25 + -22.5w + 2w2 = 10.5 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
33.25 + -22.5w + 2w2 = 0.0

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

Divide each side by '2'.
16.625 + -11.25w + w2 = 0.0

Move the constant term to the right:

Add '-16.625' to each side of the equation.
16.625 + -11.25w + -16.625 + w2 = 0.0 + -16.625

Reorder the terms:
16.625 + -16.625 + -11.25w + w2 = 0.0 + -16.625

Combine like terms: 16.625 + -16.625 = 0.000
0.000 + -11.25w + w2 = 0.0 + -16.625
-11.25w + w2 = 0.0 + -16.625

Combine like terms: 0.0 + -16.625 = -16.625
-11.25w + w2 = -16.625

The w term is -11.25w.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25w + 31.640625 + w2 = -16.625 + 31.640625

Reorder the terms:
31.640625 + -11.25w + w2 = -16.625 + 31.640625

Combine like terms: -16.625 + 31.640625 = 15.015625
31.640625 + -11.25w + w2 = 15.015625

Factor a perfect square on the left side:
(w + -5.625)(w + -5.625) = 15.015625

Calculate the square root of the right side: 3.875

Break this problem into two subproblems by setting 
(w + -5.625) equal to 3.875 and -3.875.

Subproblem 1

w + -5.625 = 3.875 Simplifying w + -5.625 = 3.875 Reorder the terms: -5.625 + w = 3.875 Solving -5.625 + w = 3.875 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + w = 3.875 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + w = 3.875 + 5.625 w = 3.875 + 5.625 Combine like terms: 3.875 + 5.625 = 9.5 w = 9.5 Simplifying w = 9.5

Subproblem 2

w + -5.625 = -3.875 Simplifying w + -5.625 = -3.875 Reorder the terms: -5.625 + w = -3.875 Solving -5.625 + w = -3.875 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + w = -3.875 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + w = -3.875 + 5.625 w = -3.875 + 5.625 Combine like terms: -3.875 + 5.625 = 1.75 w = 1.75 Simplifying w = 1.75

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.5, 1.75}

See similar equations:

| d(x)=40(0.85) | | 2x^2-20x+37=0 | | 4x+10-3x=2+12 | | X=-7.6+-0.4x | | (9+w)(2w+7)=0 | | 4y-3x=-19 | | C=2*pi*12 | | 2x-19=25 | | 5(n-4)=-15 | | -1-3v+4v=4v+2 | | 7K+6=3K+18 | | 1.13+0.13k=k | | 7p-7=-3p+5 | | 4u+13=6u+7 | | 8x+12(2+3x)=16(1+4x) | | fraction=3 | | y=-69 | | 3.2x+4.8=9.6 | | ln^2+lnx-90=0 | | 4x^2+10x-66=0 | | 8+3B=14+5B | | 8k+2=K+11 | | 4x-12+x+17=180 | | x+0.24x=49 | | f(x)=3x^2-7x-6 | | 3(2x+1)=7x-3x+4 | | 5-6x=-8x-3 | | 10x=2x+60 | | 3p+35=128 | | X+2.5=2.5x | | x+0.24x=29 | | 9K+3.5=K+6 |

Equations solver categories