3w^2-.75w=.5

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Solution for 3w^2-.75w=.5 equation:


Simplifying
3w2 + -0.75w = 0.5

Reorder the terms:
-0.75w + 3w2 = 0.5

Solving
-0.75w + 3w2 = 0.5

Solving for variable 'w'.

Reorder the terms:
-0.5 + -0.75w + 3w2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + -0.75w + 3w2 = 0.0

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

Divide each side by '3'.
-0.1666666667 + -0.25w + w2 = 0.0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.25w + 0.1666666667 + w2 = 0.0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.25w + w2 = 0.0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.25w + w2 = 0.0 + 0.1666666667
-0.25w + w2 = 0.0 + 0.1666666667

Combine like terms: 0.0 + 0.1666666667 = 0.1666666667
-0.25w + w2 = 0.1666666667

The w term is -0.25w.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25w + 0.015625 + w2 = 0.1666666667 + 0.015625

Reorder the terms:
0.015625 + -0.25w + w2 = 0.1666666667 + 0.015625

Combine like terms: 0.1666666667 + 0.015625 = 0.1822916667
0.015625 + -0.25w + w2 = 0.1822916667

Factor a perfect square on the left side:
(w + -0.125)(w + -0.125) = 0.1822916667

Calculate the square root of the right side: 0.426956282

Break this problem into two subproblems by setting 
(w + -0.125) equal to 0.426956282 and -0.426956282.

Subproblem 1

w + -0.125 = 0.426956282 Simplifying w + -0.125 = 0.426956282 Reorder the terms: -0.125 + w = 0.426956282 Solving -0.125 + w = 0.426956282 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = 0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = 0.426956282 + 0.125 w = 0.426956282 + 0.125 Combine like terms: 0.426956282 + 0.125 = 0.551956282 w = 0.551956282 Simplifying w = 0.551956282

Subproblem 2

w + -0.125 = -0.426956282 Simplifying w + -0.125 = -0.426956282 Reorder the terms: -0.125 + w = -0.426956282 Solving -0.125 + w = -0.426956282 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = -0.426956282 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = -0.426956282 + 0.125 w = -0.426956282 + 0.125 Combine like terms: -0.426956282 + 0.125 = -0.301956282 w = -0.301956282 Simplifying w = -0.301956282

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.551956282, -0.301956282}

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