w^2-10w=43

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Solution for w^2-10w=43 equation:


Simplifying
w2 + -10w = 43

Reorder the terms:
-10w + w2 = 43

Solving
-10w + w2 = 43

Solving for variable 'w'.

Reorder the terms:
-43 + -10w + w2 = 43 + -43

Combine like terms: 43 + -43 = 0
-43 + -10w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -10w + 43 + w2 = 0 + 43

Reorder the terms:
-43 + 43 + -10w + w2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -10w + w2 = 0 + 43
-10w + w2 = 0 + 43

Combine like terms: 0 + 43 = 43
-10w + w2 = 43

The w term is -10w.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10w + 25 + w2 = 43 + 25

Reorder the terms:
25 + -10w + w2 = 43 + 25

Combine like terms: 43 + 25 = 68
25 + -10w + w2 = 68

Factor a perfect square on the left side:
(w + -5)(w + -5) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(w + -5) equal to 8.246211251 and -8.246211251.

Subproblem 1

w + -5 = 8.246211251 Simplifying w + -5 = 8.246211251 Reorder the terms: -5 + w = 8.246211251 Solving -5 + w = 8.246211251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 8.246211251 + 5 Combine like terms: -5 + 5 = 0 0 + w = 8.246211251 + 5 w = 8.246211251 + 5 Combine like terms: 8.246211251 + 5 = 13.246211251 w = 13.246211251 Simplifying w = 13.246211251

Subproblem 2

w + -5 = -8.246211251 Simplifying w + -5 = -8.246211251 Reorder the terms: -5 + w = -8.246211251 Solving -5 + w = -8.246211251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -8.246211251 + 5 Combine like terms: -5 + 5 = 0 0 + w = -8.246211251 + 5 w = -8.246211251 + 5 Combine like terms: -8.246211251 + 5 = -3.246211251 w = -3.246211251 Simplifying w = -3.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. w = {13.246211251, -3.246211251}

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