w^2-8w=7

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Solution for w^2-8w=7 equation:


Simplifying
w2 + -8w = 7

Reorder the terms:
-8w + w2 = 7

Solving
-8w + w2 = 7

Solving for variable 'w'.

Reorder the terms:
-7 + -8w + w2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -8w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8w + 7 + w2 = 0 + 7

Reorder the terms:
-7 + 7 + -8w + w2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8w + w2 = 0 + 7
-8w + w2 = 0 + 7

Combine like terms: 0 + 7 = 7
-8w + w2 = 7

The w term is -8w.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8w + 16 + w2 = 7 + 16

Reorder the terms:
16 + -8w + w2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8w + w2 = 23

Factor a perfect square on the left side:
(w + -4)(w + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(w + -4) equal to 4.795831523 and -4.795831523.

Subproblem 1

w + -4 = 4.795831523 Simplifying w + -4 = 4.795831523 Reorder the terms: -4 + w = 4.795831523 Solving -4 + w = 4.795831523 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + w = 4.795831523 + 4 w = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 w = 8.795831523 Simplifying w = 8.795831523

Subproblem 2

w + -4 = -4.795831523 Simplifying w + -4 = -4.795831523 Reorder the terms: -4 + w = -4.795831523 Solving -4 + w = -4.795831523 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + w = -4.795831523 + 4 w = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 w = -0.795831523 Simplifying w = -0.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. w = {8.795831523, -0.795831523}

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