(m-4)(m-4)=7

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Solution for (m-4)(m-4)=7 equation:


Simplifying
(m + -4)(m + -4) = 7

Reorder the terms:
(-4 + m)(m + -4) = 7

Reorder the terms:
(-4 + m)(-4 + m) = 7

Multiply (-4 + m) * (-4 + m)
(-4(-4 + m) + m(-4 + m)) = 7
((-4 * -4 + m * -4) + m(-4 + m)) = 7
((16 + -4m) + m(-4 + m)) = 7
(16 + -4m + (-4 * m + m * m)) = 7
(16 + -4m + (-4m + m2)) = 7

Combine like terms: -4m + -4m = -8m
(16 + -8m + m2) = 7

Solving
16 + -8m + m2 = 7

Solving for variable 'm'.

Reorder the terms:
16 + -7 + -8m + m2 = 7 + -7

Combine like terms: 16 + -7 = 9
9 + -8m + m2 = 7 + -7

Combine like terms: 7 + -7 = 0
9 + -8m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8m + -9 + m2 = 0 + -9

Reorder the terms:
9 + -9 + -8m + m2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8m + m2 = 0 + -9
-8m + m2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8m + m2 = -9

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

Add '16' to each side of the equation.
-8m + 16 + m2 = -9 + 16

Reorder the terms:
16 + -8m + m2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8m + m2 = 7

Factor a perfect square on the left side:
(m + -4)(m + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(m + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1

m + -4 = 2.645751311 Simplifying m + -4 = 2.645751311 Reorder the terms: -4 + m = 2.645751311 Solving -4 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + m = 2.645751311 + 4 m = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 m = 6.645751311 Simplifying m = 6.645751311

Subproblem 2

m + -4 = -2.645751311 Simplifying m + -4 = -2.645751311 Reorder the terms: -4 + m = -2.645751311 Solving -4 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + m = -2.645751311 + 4 m = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 m = 1.354248689 Simplifying m = 1.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.645751311, 1.354248689}

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