7x^2-4x-1512=0

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Solution for 7x^2-4x-1512=0 equation: 


Simplifying
7x2 + -4x + -1512 = 0

Reorder the terms:
-1512 + -4x + 7x2 = 0

Solving
-1512 + -4x + 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'.
-216 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + -0.5714285714x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + -0.5714285714x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + -0.5714285714x + x2 = 0 + 216
-0.5714285714x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
-0.5714285714x + x2 = 216

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 216 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 216 + 0.08163265305

Combine like terms: 216 + 0.08163265305 = 216.08163265305
0.08163265305 + -0.5714285714x + x2 = 216.08163265305

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 216.08163265305

Calculate the square root of the right side: 14.699715394

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 14.699715394 and -14.699715394.


Subproblem 1
x + -0.2857142857 = 14.699715394

Simplifying
x + -0.2857142857 = 14.699715394

Reorder the terms:
-0.2857142857 + x = 14.699715394

Solving
-0.2857142857 + x = 14.699715394

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = 14.699715394 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = 14.699715394 + 0.2857142857
x = 14.699715394 + 0.2857142857

Combine like terms: 14.699715394 + 0.2857142857 = 14.9854296797
x = 14.9854296797

Simplifying
x = 14.9854296797


Subproblem 2
x + -0.2857142857 = -14.699715394

Simplifying
x + -0.2857142857 = -14.699715394

Reorder the terms:
-0.2857142857 + x = -14.699715394

Solving
-0.2857142857 + x = -14.699715394

Solving for variable 'x'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = -14.699715394 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = -14.699715394 + 0.2857142857
x = -14.699715394 + 0.2857142857

Combine like terms: -14.699715394 + 0.2857142857 = -14.4140011083
x = -14.4140011083

Simplifying
x = -14.4140011083


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.9854296797, -14.4140011083}

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