.5x^2+3x=14

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Solution for .5x^2+3x=14 equation:


Simplifying
0.5x2 + 3x = 14

Reorder the terms:
3x + 0.5x2 = 14

Solving
3x + 0.5x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 3x + 0.5x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 3x + 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'.
-28 + 6x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 6x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 6x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 6x + x2 = 0 + 28
6x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
6x + x2 = 28

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 28 + 9

Reorder the terms:
9 + 6x + x2 = 28 + 9

Combine like terms: 28 + 9 = 37
9 + 6x + x2 = 37

Factor a perfect square on the left side:
(x + 3)(x + 3) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 3) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + 3 = 6.08276253 Simplifying x + 3 = 6.08276253 Reorder the terms: 3 + x = 6.08276253 Solving 3 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.08276253 + -3 x = 6.08276253 + -3 Combine like terms: 6.08276253 + -3 = 3.08276253 x = 3.08276253 Simplifying x = 3.08276253

Subproblem 2

x + 3 = -6.08276253 Simplifying x + 3 = -6.08276253 Reorder the terms: 3 + x = -6.08276253 Solving 3 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.08276253 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.08276253 + -3 x = -6.08276253 + -3 Combine like terms: -6.08276253 + -3 = -9.08276253 x = -9.08276253 Simplifying x = -9.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.08276253, -9.08276253}

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