15x^2-4x-7=0

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Solution for 15x^2-4x-7=0 equation: 


Simplifying
15x2 + -4x + -7 = 0

Reorder the terms:
-7 + -4x + 15x2 = 0

Solving
-7 + -4x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.4666666667 + -0.2666666667x + x2 = 0

Move the constant term to the right:

Add '0.4666666667' to each side of the equation.
-0.4666666667 + -0.2666666667x + 0.4666666667 + x2 = 0 + 0.4666666667

Reorder the terms:
-0.4666666667 + 0.4666666667 + -0.2666666667x + x2 = 0 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + -0.2666666667x + x2 = 0 + 0.4666666667
-0.2666666667x + x2 = 0 + 0.4666666667

Combine like terms: 0 + 0.4666666667 = 0.4666666667
-0.2666666667x + x2 = 0.4666666667

The x term is -0.2666666667x.  Take half its coefficient (-0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
-0.2666666667x + 0.01777777780 + x2 = 0.4666666667 + 0.01777777780

Reorder the terms:
0.01777777780 + -0.2666666667x + x2 = 0.4666666667 + 0.01777777780

Combine like terms: 0.4666666667 + 0.01777777780 = 0.4844444445
0.01777777780 + -0.2666666667x + x2 = 0.4844444445

Factor a perfect square on the left side:
(x + -0.1333333334)(x + -0.1333333334) = 0.4844444445

Calculate the square root of the right side: 0.696020434

Break this problem into two subproblems by setting 
(x + -0.1333333334) equal to 0.696020434 and -0.696020434.


Subproblem 1
x + -0.1333333334 = 0.696020434

Simplifying
x + -0.1333333334 = 0.696020434

Reorder the terms:
-0.1333333334 + x = 0.696020434

Solving
-0.1333333334 + x = 0.696020434

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.1333333334' to each side of the equation.
-0.1333333334 + 0.1333333334 + x = 0.696020434 + 0.1333333334

Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000
0.0000000000 + x = 0.696020434 + 0.1333333334
x = 0.696020434 + 0.1333333334

Combine like terms: 0.696020434 + 0.1333333334 = 0.8293537674
x = 0.8293537674

Simplifying
x = 0.8293537674


Subproblem 2
x + -0.1333333334 = -0.696020434

Simplifying
x + -0.1333333334 = -0.696020434

Reorder the terms:
-0.1333333334 + x = -0.696020434

Solving
-0.1333333334 + x = -0.696020434

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.1333333334' to each side of the equation.
-0.1333333334 + 0.1333333334 + x = -0.696020434 + 0.1333333334

Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000
0.0000000000 + x = -0.696020434 + 0.1333333334
x = -0.696020434 + 0.1333333334

Combine like terms: -0.696020434 + 0.1333333334 = -0.5626871006
x = -0.5626871006

Simplifying
x = -0.5626871006


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8293537674, -0.5626871006}

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