d^2+24d+7=0

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Solution for d^2+24d+7=0 equation:


Simplifying
d2 + 24d + 7 = 0

Reorder the terms:
7 + 24d + d2 = 0

Solving
7 + 24d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 24d + -7 + d2 = 0 + -7

Reorder the terms:
7 + -7 + 24d + d2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 24d + d2 = 0 + -7
24d + d2 = 0 + -7

Combine like terms: 0 + -7 = -7
24d + d2 = -7

The d term is 24d.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24d + 144 + d2 = -7 + 144

Reorder the terms:
144 + 24d + d2 = -7 + 144

Combine like terms: -7 + 144 = 137
144 + 24d + d2 = 137

Factor a perfect square on the left side:
(d + 12)(d + 12) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(d + 12) equal to 11.704699911 and -11.704699911.

Subproblem 1

d + 12 = 11.704699911 Simplifying d + 12 = 11.704699911 Reorder the terms: 12 + d = 11.704699911 Solving 12 + d = 11.704699911 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + d = 11.704699911 + -12 Combine like terms: 12 + -12 = 0 0 + d = 11.704699911 + -12 d = 11.704699911 + -12 Combine like terms: 11.704699911 + -12 = -0.295300089 d = -0.295300089 Simplifying d = -0.295300089

Subproblem 2

d + 12 = -11.704699911 Simplifying d + 12 = -11.704699911 Reorder the terms: 12 + d = -11.704699911 Solving 12 + d = -11.704699911 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + d = -11.704699911 + -12 Combine like terms: 12 + -12 = 0 0 + d = -11.704699911 + -12 d = -11.704699911 + -12 Combine like terms: -11.704699911 + -12 = -23.704699911 d = -23.704699911 Simplifying d = -23.704699911

Solution

The solution to the problem is based on the solutions from the subproblems. d = {-0.295300089, -23.704699911}

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