h^2-8h+16=15

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Solution for h^2-8h+16=15 equation:


Simplifying
h2 + -8h + 16 = 15

Reorder the terms:
16 + -8h + h2 = 15

Solving
16 + -8h + h2 = 15

Solving for variable 'h'.

Reorder the terms:
16 + -15 + -8h + h2 = 15 + -15

Combine like terms: 16 + -15 = 1
1 + -8h + h2 = 15 + -15

Combine like terms: 15 + -15 = 0
1 + -8h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -8h + -1 + h2 = 0 + -1

Reorder the terms:
1 + -1 + -8h + h2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8h + h2 = 0 + -1
-8h + h2 = 0 + -1

Combine like terms: 0 + -1 = -1
-8h + h2 = -1

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

Add '16' to each side of the equation.
-8h + 16 + h2 = -1 + 16

Reorder the terms:
16 + -8h + h2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + -8h + h2 = 15

Factor a perfect square on the left side:
(h + -4)(h + -4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(h + -4) equal to 3.872983346 and -3.872983346.

Subproblem 1

h + -4 = 3.872983346 Simplifying h + -4 = 3.872983346 Reorder the terms: -4 + h = 3.872983346 Solving -4 + h = 3.872983346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + h = 3.872983346 + 4 h = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 h = 7.872983346 Simplifying h = 7.872983346

Subproblem 2

h + -4 = -3.872983346 Simplifying h + -4 = -3.872983346 Reorder the terms: -4 + h = -3.872983346 Solving -4 + h = -3.872983346 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + h = -3.872983346 + 4 h = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 h = 0.127016654 Simplifying h = 0.127016654

Solution

The solution to the problem is based on the solutions from the subproblems. h = {7.872983346, 0.127016654}

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