x^2+16*x+1.2=0

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Solution for x^2+16*x+1.2=0 equation:


Simplifying
x2 + 16x + 1.2 = 0

Reorder the terms:
1.2 + 16x + x2 = 0

Solving
1.2 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 16x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 16x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 16x + x2 = 0 + -1.2
16x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
16x + x2 = -1.2

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -1.2 + 64

Reorder the terms:
64 + 16x + x2 = -1.2 + 64

Combine like terms: -1.2 + 64 = 62.8
64 + 16x + x2 = 62.8

Factor a perfect square on the left side:
(x + 8)(x + 8) = 62.8

Calculate the square root of the right side: 7.924645102

Break this problem into two subproblems by setting 
(x + 8) equal to 7.924645102 and -7.924645102.

Subproblem 1

x + 8 = 7.924645102 Simplifying x + 8 = 7.924645102 Reorder the terms: 8 + x = 7.924645102 Solving 8 + x = 7.924645102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.924645102 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.924645102 + -8 x = 7.924645102 + -8 Combine like terms: 7.924645102 + -8 = -0.075354898 x = -0.075354898 Simplifying x = -0.075354898

Subproblem 2

x + 8 = -7.924645102 Simplifying x + 8 = -7.924645102 Reorder the terms: 8 + x = -7.924645102 Solving 8 + x = -7.924645102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.924645102 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.924645102 + -8 x = -7.924645102 + -8 Combine like terms: -7.924645102 + -8 = -15.924645102 x = -15.924645102 Simplifying x = -15.924645102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.075354898, -15.924645102}

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