w^2-3w-64=0

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Solution for w^2-3w-64=0 equation:


Simplifying
w2 + -3w + -64 = 0

Reorder the terms:
-64 + -3w + w2 = 0

Solving
-64 + -3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -3w + 64 + w2 = 0 + 64

Reorder the terms:
-64 + 64 + -3w + w2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -3w + w2 = 0 + 64
-3w + w2 = 0 + 64

Combine like terms: 0 + 64 = 64
-3w + w2 = 64

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = 64 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 64 + 2.25

Combine like terms: 64 + 2.25 = 66.25
2.25 + -3w + w2 = 66.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(w + -1.5) equal to 8.139410298 and -8.139410298.

Subproblem 1

w + -1.5 = 8.139410298 Simplifying w + -1.5 = 8.139410298 Reorder the terms: -1.5 + w = 8.139410298 Solving -1.5 + w = 8.139410298 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 8.139410298 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 8.139410298 + 1.5 w = 8.139410298 + 1.5 Combine like terms: 8.139410298 + 1.5 = 9.639410298 w = 9.639410298 Simplifying w = 9.639410298

Subproblem 2

w + -1.5 = -8.139410298 Simplifying w + -1.5 = -8.139410298 Reorder the terms: -1.5 + w = -8.139410298 Solving -1.5 + w = -8.139410298 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -8.139410298 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -8.139410298 + 1.5 w = -8.139410298 + 1.5 Combine like terms: -8.139410298 + 1.5 = -6.639410298 w = -6.639410298 Simplifying w = -6.639410298

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.639410298, -6.639410298}

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