.5x^2+6x=31

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Solution for .5x^2+6x=31 equation:


Simplifying
0.5x2 + 6x = 31

Reorder the terms:
6x + 0.5x2 = 31

Solving
6x + 0.5x2 = 31

Solving for variable 'x'.

Reorder the terms:
-31 + 6x + 0.5x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 6x + 0.5x2 = 0

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

Divide each side by '0.5'.
-62 + 12x + x2 = 0

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + 12x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + 12x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + 12x + x2 = 0 + 62
12x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
12x + x2 = 62

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 62 + 36

Reorder the terms:
36 + 12x + x2 = 62 + 36

Combine like terms: 62 + 36 = 98
36 + 12x + x2 = 98

Factor a perfect square on the left side:
(x + 6)(x + 6) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + 6) equal to 9.899494937 and -9.899494937.

Subproblem 1

x + 6 = 9.899494937 Simplifying x + 6 = 9.899494937 Reorder the terms: 6 + x = 9.899494937 Solving 6 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 9.899494937 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.899494937 + -6 x = 9.899494937 + -6 Combine like terms: 9.899494937 + -6 = 3.899494937 x = 3.899494937 Simplifying x = 3.899494937

Subproblem 2

x + 6 = -9.899494937 Simplifying x + 6 = -9.899494937 Reorder the terms: 6 + x = -9.899494937 Solving 6 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -9.899494937 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.899494937 + -6 x = -9.899494937 + -6 Combine like terms: -9.899494937 + -6 = -15.899494937 x = -15.899494937 Simplifying x = -15.899494937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.899494937, -15.899494937}

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