w^2=4w+3

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Solution for w^2=4w+3 equation:


Simplifying
w2 = 4w + 3

Reorder the terms:
w2 = 3 + 4w

Solving
w2 = 3 + 4w

Solving for variable 'w'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + -4w + w2 = 0 + 3

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

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

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = 3 + 4

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

Combine like terms: 3 + 4 = 7
4 + -4w + w2 = 7

Factor a perfect square on the left side:
(w + -2)(w + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(w + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1

w + -2 = 2.645751311 Simplifying w + -2 = 2.645751311 Reorder the terms: -2 + w = 2.645751311 Solving -2 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + w = 2.645751311 + 2 w = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 w = 4.645751311 Simplifying w = 4.645751311

Subproblem 2

w + -2 = -2.645751311 Simplifying w + -2 = -2.645751311 Reorder the terms: -2 + w = -2.645751311 Solving -2 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + w = -2.645751311 + 2 w = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 w = -0.645751311 Simplifying w = -0.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.645751311, -0.645751311}

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