10x^2+3x-36=0

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Solution for 10x^2+3x-36=0 equation:


Simplifying
10x2 + 3x + -36 = 0

Reorder the terms:
-36 + 3x + 10x2 = 0

Solving
-36 + 3x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-3.6 + 0.3x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 0.3x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 0.3x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 0.3x + x2 = 0 + 3.6
0.3x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
0.3x + x2 = 3.6

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 3.6 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 3.6 + 0.0225

Combine like terms: 3.6 + 0.0225 = 3.6225
0.0225 + 0.3x + x2 = 3.6225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 3.6225

Calculate the square root of the right side: 1.903286631

Break this problem into two subproblems by setting 
(x + 0.15) equal to 1.903286631 and -1.903286631.

Subproblem 1

x + 0.15 = 1.903286631 Simplifying x + 0.15 = 1.903286631 Reorder the terms: 0.15 + x = 1.903286631 Solving 0.15 + x = 1.903286631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 1.903286631 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.903286631 + -0.15 x = 1.903286631 + -0.15 Combine like terms: 1.903286631 + -0.15 = 1.753286631 x = 1.753286631 Simplifying x = 1.753286631

Subproblem 2

x + 0.15 = -1.903286631 Simplifying x + 0.15 = -1.903286631 Reorder the terms: 0.15 + x = -1.903286631 Solving 0.15 + x = -1.903286631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -1.903286631 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.903286631 + -0.15 x = -1.903286631 + -0.15 Combine like terms: -1.903286631 + -0.15 = -2.053286631 x = -2.053286631 Simplifying x = -2.053286631

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.753286631, -2.053286631}

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