d^2+10d+25=7

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Solution for d^2+10d+25=7 equation:


Simplifying
d2 + 10d + 25 = 7

Reorder the terms:
25 + 10d + d2 = 7

Solving
25 + 10d + d2 = 7

Solving for variable 'd'.

Reorder the terms:
25 + -7 + 10d + d2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + 10d + d2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + 10d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10d + -18 + d2 = 0 + -18

Reorder the terms:
18 + -18 + 10d + d2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10d + d2 = 0 + -18
10d + d2 = 0 + -18

Combine like terms: 0 + -18 = -18
10d + d2 = -18

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 = -18 + 25

Reorder the terms:
25 + 10d + d2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10d + d2 = 7

Factor a perfect square on the left side:
(d + 5)(d + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(d + 5) equal to 2.645751311 and -2.645751311.

Subproblem 1

d + 5 = 2.645751311 Simplifying d + 5 = 2.645751311 Reorder the terms: 5 + d = 2.645751311 Solving 5 + d = 2.645751311 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 = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + d = 2.645751311 + -5 d = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 d = -2.354248689 Simplifying d = -2.354248689

Subproblem 2

d + 5 = -2.645751311 Simplifying d + 5 = -2.645751311 Reorder the terms: 5 + d = -2.645751311 Solving 5 + d = -2.645751311 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 = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + d = -2.645751311 + -5 d = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 d = -7.645751311 Simplifying d = -7.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. d = {-2.354248689, -7.645751311}

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