0.5x^2+4x+3=0

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Solution for 0.5x^2+4x+3=0 equation:


Simplifying
0.5x2 + 4x + 3 = 0

Reorder the terms:
3 + 4x + 0.5x2 = 0

Solving
3 + 4x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
6 + 8x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8x + x2 = 0 + -6
8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
8x + x2 = -6

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -6 + 16

Reorder the terms:
16 + 8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8x + x2 = 10

Factor a perfect square on the left side:
(x + 4)(x + 4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 4) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 4 = 3.16227766 Simplifying x + 4 = 3.16227766 Reorder the terms: 4 + x = 3.16227766 Solving 4 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.16227766 + -4 x = 3.16227766 + -4 Combine like terms: 3.16227766 + -4 = -0.83772234 x = -0.83772234 Simplifying x = -0.83772234

Subproblem 2

x + 4 = -3.16227766 Simplifying x + 4 = -3.16227766 Reorder the terms: 4 + x = -3.16227766 Solving 4 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.16227766 + -4 x = -3.16227766 + -4 Combine like terms: -3.16227766 + -4 = -7.16227766 x = -7.16227766 Simplifying x = -7.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.83772234, -7.16227766}

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