12x^2+2x-15=0

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Solution for 12x^2+2x-15=0 equation:


Simplifying
12x2 + 2x + -15 = 0

Reorder the terms:
-15 + 2x + 12x2 = 0

Solving
-15 + 2x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-1.25 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.1666666667x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.1666666667x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.1666666667x + x2 = 0 + 1.25
0.1666666667x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.1666666667x + x2 = 1.25

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 1.25 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 1.25 + 0.006944444447

Combine like terms: 1.25 + 0.006944444447 = 1.256944444447
0.006944444447 + 0.1666666667x + x2 = 1.256944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 1.256944444447

Calculate the square root of the right side: 1.121135337

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 1.121135337 and -1.121135337.

Subproblem 1

x + 0.08333333335 = 1.121135337 Simplifying x + 0.08333333335 = 1.121135337 Reorder the terms: 0.08333333335 + x = 1.121135337 Solving 0.08333333335 + x = 1.121135337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.121135337 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.121135337 + -0.08333333335 x = 1.121135337 + -0.08333333335 Combine like terms: 1.121135337 + -0.08333333335 = 1.03780200365 x = 1.03780200365 Simplifying x = 1.03780200365

Subproblem 2

x + 0.08333333335 = -1.121135337 Simplifying x + 0.08333333335 = -1.121135337 Reorder the terms: 0.08333333335 + x = -1.121135337 Solving 0.08333333335 + x = -1.121135337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.121135337 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.121135337 + -0.08333333335 x = -1.121135337 + -0.08333333335 Combine like terms: -1.121135337 + -0.08333333335 = -1.20446867035 x = -1.20446867035 Simplifying x = -1.20446867035

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.03780200365, -1.20446867035}

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