d^2-10d+1=0

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Solution for d^2-10d+1=0 equation:


Simplifying
d2 + -10d + 1 = 0

Reorder the terms:
1 + -10d + d2 = 0

Solving
1 + -10d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10d + -1 + d2 = 0 + -1

Reorder the terms:
1 + -1 + -10d + d2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10d + d2 = 0 + -1
-10d + d2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10d + d2 = -1

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

Add '25' to each side of the equation.
-10d + 25 + d2 = -1 + 25

Reorder the terms:
25 + -10d + d2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + -10d + d2 = 24

Factor a perfect square on the left side:
(d + -5)(d + -5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(d + -5) equal to 4.898979486 and -4.898979486.

Subproblem 1

d + -5 = 4.898979486 Simplifying d + -5 = 4.898979486 Reorder the terms: -5 + d = 4.898979486 Solving -5 + d = 4.898979486 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + d = 4.898979486 + 5 d = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 d = 9.898979486 Simplifying d = 9.898979486

Subproblem 2

d + -5 = -4.898979486 Simplifying d + -5 = -4.898979486 Reorder the terms: -5 + d = -4.898979486 Solving -5 + d = -4.898979486 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + d = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + d = -4.898979486 + 5 d = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 d = 0.101020514 Simplifying d = 0.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. d = {9.898979486, 0.101020514}

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