3.14d^2+7*3.14d+12*3.14=0

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Solution for 3.14d^2+7*3.14d+12*3.14=0 equation:


Simplifying
3.14d2 + 7 * 3.14d + 12 * 3.14 = 0

Multiply 7 * 3.14
3.14d2 + 21.98d + 12 * 3.14 = 0

Multiply 12 * 3.14
3.14d2 + 21.98d + 37.68 = 0

Reorder the terms:
37.68 + 21.98d + 3.14d2 = 0

Solving
37.68 + 21.98d + 3.14d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
3.14 the coefficient of the squared term: 

Divide each side by '3.14'.
12 + 7d + d2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 7d + -12 + d2 = 0 + -12

Reorder the terms:
12 + -12 + 7d + d2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 7d + d2 = 0 + -12
7d + d2 = 0 + -12

Combine like terms: 0 + -12 = -12
7d + d2 = -12

The d term is 7d.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7d + 12.25 + d2 = -12 + 12.25

Reorder the terms:
12.25 + 7d + d2 = -12 + 12.25

Combine like terms: -12 + 12.25 = 0.25
12.25 + 7d + d2 = 0.25

Factor a perfect square on the left side:
(d + 3.5)(d + 3.5) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(d + 3.5) equal to 0.5 and -0.5.

Subproblem 1

d + 3.5 = 0.5 Simplifying d + 3.5 = 0.5 Reorder the terms: 3.5 + d = 0.5 Solving 3.5 + d = 0.5 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = 0.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = 0.5 + -3.5 d = 0.5 + -3.5 Combine like terms: 0.5 + -3.5 = -3 d = -3 Simplifying d = -3

Subproblem 2

d + 3.5 = -0.5 Simplifying d + 3.5 = -0.5 Reorder the terms: 3.5 + d = -0.5 Solving 3.5 + d = -0.5 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + d = -0.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + d = -0.5 + -3.5 d = -0.5 + -3.5 Combine like terms: -0.5 + -3.5 = -4 d = -4 Simplifying d = -4

Solution

The solution to the problem is based on the solutions from the subproblems. d = {-3, -4}

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