7x^2-2x-36=0

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Solution for 7x^2-2x-36=0 equation:


Simplifying
7x2 + -2x + -36 = 0

Reorder the terms:
-36 + -2x + 7x2 = 0

Solving
-36 + -2x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-5.142857143 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '5.142857143' to each side of the equation.
-5.142857143 + -0.2857142857x + 5.142857143 + x2 = 0 + 5.142857143

Reorder the terms:
-5.142857143 + 5.142857143 + -0.2857142857x + x2 = 0 + 5.142857143

Combine like terms: -5.142857143 + 5.142857143 = 0.000000000
0.000000000 + -0.2857142857x + x2 = 0 + 5.142857143
-0.2857142857x + x2 = 0 + 5.142857143

Combine like terms: 0 + 5.142857143 = 5.142857143
-0.2857142857x + x2 = 5.142857143

The x term is -0.2857142857x.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857x + 0.02040816328 + x2 = 5.142857143 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 5.142857143 + 0.02040816328

Combine like terms: 5.142857143 + 0.02040816328 = 5.16326530628
0.02040816328 + -0.2857142857x + x2 = 5.16326530628

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 5.16326530628

Calculate the square root of the right side: 2.27228196

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 2.27228196 and -2.27228196.

Subproblem 1

x + -0.1428571429 = 2.27228196 Simplifying x + -0.1428571429 = 2.27228196 Reorder the terms: -0.1428571429 + x = 2.27228196 Solving -0.1428571429 + x = 2.27228196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 2.27228196 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 2.27228196 + 0.1428571429 x = 2.27228196 + 0.1428571429 Combine like terms: 2.27228196 + 0.1428571429 = 2.4151391029 x = 2.4151391029 Simplifying x = 2.4151391029

Subproblem 2

x + -0.1428571429 = -2.27228196 Simplifying x + -0.1428571429 = -2.27228196 Reorder the terms: -0.1428571429 + x = -2.27228196 Solving -0.1428571429 + x = -2.27228196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -2.27228196 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -2.27228196 + 0.1428571429 x = -2.27228196 + 0.1428571429 Combine like terms: -2.27228196 + 0.1428571429 = -2.1294248171 x = -2.1294248171 Simplifying x = -2.1294248171

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4151391029, -2.1294248171}

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