d^2-8d+16=11

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Solution for d^2-8d+16=11 equation:


Simplifying
d2 + -8d + 16 = 11

Reorder the terms:
16 + -8d + d2 = 11

Solving
16 + -8d + d2 = 11

Solving for variable 'd'.

Reorder the terms:
16 + -11 + -8d + d2 = 11 + -11

Combine like terms: 16 + -11 = 5
5 + -8d + d2 = 11 + -11

Combine like terms: 11 + -11 = 0
5 + -8d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8d + -5 + d2 = 0 + -5

Reorder the terms:
5 + -5 + -8d + d2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8d + d2 = 0 + -5
-8d + d2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8d + d2 = -5

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

Add '16' to each side of the equation.
-8d + 16 + d2 = -5 + 16

Reorder the terms:
16 + -8d + d2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8d + d2 = 11

Factor a perfect square on the left side:
(d + -4)(d + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(d + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1

d + -4 = 3.31662479 Simplifying d + -4 = 3.31662479 Reorder the terms: -4 + d = 3.31662479 Solving -4 + d = 3.31662479 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + d = 3.31662479 + 4 d = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 d = 7.31662479 Simplifying d = 7.31662479

Subproblem 2

d + -4 = -3.31662479 Simplifying d + -4 = -3.31662479 Reorder the terms: -4 + d = -3.31662479 Solving -4 + d = -3.31662479 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + d = -3.31662479 + 4 d = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 d = 0.68337521 Simplifying d = 0.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. d = {7.31662479, 0.68337521}

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