(10000000)(x^2)+13x-1.3=0

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Solution for (10000000)(x^2)+13x-1.3=0 equation:


Simplifying
(10000000)(x2) + 13x + -1.3 = 0

Reorder the terms:
-1.3 + 13x + 10000000x2 = 0

Solving
-1.3 + 13x + 10000000x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
10000000 the coefficient of the squared term: 

Divide each side by '10000000'.
-0.00000013 + 0.0000013x + x2 = 0

Move the constant term to the right:

Add '0.00000013' to each side of the equation.
-0.00000013 + 0.0000013x + 0.00000013 + x2 = 0 + 0.00000013

Reorder the terms:
-0.00000013 + 0.00000013 + 0.0000013x + x2 = 0 + 0.00000013

Combine like terms: -0.00000013 + 0.00000013 = 0.00000000
0.00000000 + 0.0000013x + x2 = 0 + 0.00000013
0.0000013x + x2 = 0 + 0.00000013

Combine like terms: 0 + 0.00000013 = 0.00000013
0.0000013x + x2 = 0.00000013

The x term is 0.0000013x.  Take half its coefficient (0.00000065).
Square it (0.0000000000004225) and add it to both sides.

Add '0.0000000000004225' to each side of the equation.
0.0000013x + 0.0000000000004225 + x2 = 0.00000013 + 0.0000000000004225

Reorder the terms:
0.0000000000004225 + 0.0000013x + x2 = 0.00000013 + 0.0000000000004225

Combine like terms: 0.00000013 + 0.0000000000004225 = 0.0000001300004225
0.0000000000004225 + 0.0000013x + x2 = 0.0000001300004225

Factor a perfect square on the left side:
(x + 0.00000065)(x + 0.00000065) = 0.0000001300004225

Calculate the square root of the right side: 0.000360556

Break this problem into two subproblems by setting 
(x + 0.00000065) equal to 0.000360556 and -0.000360556.

Subproblem 1

x + 0.00000065 = 0.000360556 Simplifying x + 0.00000065 = 0.000360556 Reorder the terms: 0.00000065 + x = 0.000360556 Solving 0.00000065 + x = 0.000360556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000065' to each side of the equation. 0.00000065 + -0.00000065 + x = 0.000360556 + -0.00000065 Combine like terms: 0.00000065 + -0.00000065 = 0.00000000 0.00000000 + x = 0.000360556 + -0.00000065 x = 0.000360556 + -0.00000065 Combine like terms: 0.000360556 + -0.00000065 = 0.000359906 x = 0.000359906 Simplifying x = 0.000359906

Subproblem 2

x + 0.00000065 = -0.000360556 Simplifying x + 0.00000065 = -0.000360556 Reorder the terms: 0.00000065 + x = -0.000360556 Solving 0.00000065 + x = -0.000360556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00000065' to each side of the equation. 0.00000065 + -0.00000065 + x = -0.000360556 + -0.00000065 Combine like terms: 0.00000065 + -0.00000065 = 0.00000000 0.00000000 + x = -0.000360556 + -0.00000065 x = -0.000360556 + -0.00000065 Combine like terms: -0.000360556 + -0.00000065 = -0.000361206 x = -0.000361206 Simplifying x = -0.000361206

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.000359906, -0.000361206}

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