3w^2-5w=4

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Solution for 3w^2-5w=4 equation:


Simplifying
3w2 + -5w = 4

Reorder the terms:
-5w + 3w2 = 4

Solving
-5w + 3w2 = 4

Solving for variable 'w'.

Reorder the terms:
-4 + -5w + 3w2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -5w + 3w2 = 0

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

Divide each side by '3'.
-1.333333333 + -1.666666667w + w2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.666666667w + 1.333333333 + w2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.666666667w + w2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.666666667w + w2 = 0 + 1.333333333
-1.666666667w + w2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.666666667w + w2 = 1.333333333

The w term is -1.666666667w.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667w + 0.6944444447 + w2 = 1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667w + w2 = 1.333333333 + 0.6944444447

Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777
0.6944444447 + -1.666666667w + w2 = 2.0277777777

Factor a perfect square on the left side:
(w + -0.8333333335)(w + -0.8333333335) = 2.0277777777

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(w + -0.8333333335) equal to 1.424000624 and -1.424000624.

Subproblem 1

w + -0.8333333335 = 1.424000624 Simplifying w + -0.8333333335 = 1.424000624 Reorder the terms: -0.8333333335 + w = 1.424000624 Solving -0.8333333335 + w = 1.424000624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = 1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = 1.424000624 + 0.8333333335 w = 1.424000624 + 0.8333333335 Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575 w = 2.2573339575 Simplifying w = 2.2573339575

Subproblem 2

w + -0.8333333335 = -1.424000624 Simplifying w + -0.8333333335 = -1.424000624 Reorder the terms: -0.8333333335 + w = -1.424000624 Solving -0.8333333335 + w = -1.424000624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = -1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = -1.424000624 + 0.8333333335 w = -1.424000624 + 0.8333333335 Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905 w = -0.5906672905 Simplifying w = -0.5906672905

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.2573339575, -0.5906672905}

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