0.5x^2+36x-310=0

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Solution for 0.5x^2+36x-310=0 equation:


Simplifying
0.5x2 + 36x + -310 = 0

Reorder the terms:
-310 + 36x + 0.5x2 = 0

Solving
-310 + 36x + 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'.
-620 + 72x + x2 = 0

Move the constant term to the right:

Add '620' to each side of the equation.
-620 + 72x + 620 + x2 = 0 + 620

Reorder the terms:
-620 + 620 + 72x + x2 = 0 + 620

Combine like terms: -620 + 620 = 0
0 + 72x + x2 = 0 + 620
72x + x2 = 0 + 620

Combine like terms: 0 + 620 = 620
72x + x2 = 620

The x term is 72x.  Take half its coefficient (36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
72x + 1296 + x2 = 620 + 1296

Reorder the terms:
1296 + 72x + x2 = 620 + 1296

Combine like terms: 620 + 1296 = 1916
1296 + 72x + x2 = 1916

Factor a perfect square on the left side:
(x + 36)(x + 36) = 1916

Calculate the square root of the right side: 43.772137256

Break this problem into two subproblems by setting 
(x + 36) equal to 43.772137256 and -43.772137256.

Subproblem 1

x + 36 = 43.772137256 Simplifying x + 36 = 43.772137256 Reorder the terms: 36 + x = 43.772137256 Solving 36 + x = 43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = 43.772137256 + -36 Combine like terms: 36 + -36 = 0 0 + x = 43.772137256 + -36 x = 43.772137256 + -36 Combine like terms: 43.772137256 + -36 = 7.772137256 x = 7.772137256 Simplifying x = 7.772137256

Subproblem 2

x + 36 = -43.772137256 Simplifying x + 36 = -43.772137256 Reorder the terms: 36 + x = -43.772137256 Solving 36 + x = -43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = -43.772137256 + -36 Combine like terms: 36 + -36 = 0 0 + x = -43.772137256 + -36 x = -43.772137256 + -36 Combine like terms: -43.772137256 + -36 = -79.772137256 x = -79.772137256 Simplifying x = -79.772137256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.772137256, -79.772137256}

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