8x^2+16x+3=0

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Solution for 8x^2+16x+3=0 equation:


Simplifying
8x2 + 16x + 3 = 0

Reorder the terms:
3 + 16x + 8x2 = 0

Solving
3 + 16x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
0.375 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 2x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 2x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 2x + x2 = 0 + -0.375
2x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
2x + x2 = -0.375

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.375 + 1

Reorder the terms:
1 + 2x + x2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + 2x + x2 = 0.625

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + 1) equal to 0.790569415 and -0.790569415.

Subproblem 1

x + 1 = 0.790569415 Simplifying x + 1 = 0.790569415 Reorder the terms: 1 + x = 0.790569415 Solving 1 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.790569415 + -1 x = 0.790569415 + -1 Combine like terms: 0.790569415 + -1 = -0.209430585 x = -0.209430585 Simplifying x = -0.209430585

Subproblem 2

x + 1 = -0.790569415 Simplifying x + 1 = -0.790569415 Reorder the terms: 1 + x = -0.790569415 Solving 1 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.790569415 + -1 x = -0.790569415 + -1 Combine like terms: -0.790569415 + -1 = -1.790569415 x = -1.790569415 Simplifying x = -1.790569415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.209430585, -1.790569415}

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