7x^2+4x-48=0

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Solution for 7x^2+4x-48=0 equation: 


Simplifying
7x2 + 4x + -48 = 0

Reorder the terms:
-48 + 4x + 7x2 = 0

Solving
-48 + 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'.
-6.857142857 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '6.857142857' to each side of the equation.
-6.857142857 + 0.5714285714x + 6.857142857 + x2 = 0 + 6.857142857

Reorder the terms:
-6.857142857 + 6.857142857 + 0.5714285714x + x2 = 0 + 6.857142857

Combine like terms: -6.857142857 + 6.857142857 = 0.000000000
0.000000000 + 0.5714285714x + x2 = 0 + 6.857142857
0.5714285714x + x2 = 0 + 6.857142857

Combine like terms: 0 + 6.857142857 = 6.857142857
0.5714285714x + x2 = 6.857142857

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 = 6.857142857 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 6.857142857 + 0.08163265305

Combine like terms: 6.857142857 + 0.08163265305 = 6.93877551005
0.08163265305 + 0.5714285714x + x2 = 6.93877551005

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 6.93877551005

Calculate the square root of the right side: 2.634155559

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 2.634155559 and -2.634155559.


Subproblem 1
x + 0.2857142857 = 2.634155559

Simplifying
x + 0.2857142857 = 2.634155559

Reorder the terms:
0.2857142857 + x = 2.634155559

Solving
0.2857142857 + x = 2.634155559

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 = 2.634155559 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 2.634155559 + -0.2857142857
x = 2.634155559 + -0.2857142857

Combine like terms: 2.634155559 + -0.2857142857 = 2.3484412733
x = 2.3484412733

Simplifying
x = 2.3484412733


Subproblem 2
x + 0.2857142857 = -2.634155559

Simplifying
x + 0.2857142857 = -2.634155559

Reorder the terms:
0.2857142857 + x = -2.634155559

Solving
0.2857142857 + x = -2.634155559

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 = -2.634155559 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -2.634155559 + -0.2857142857
x = -2.634155559 + -0.2857142857

Combine like terms: -2.634155559 + -0.2857142857 = -2.9198698447
x = -2.9198698447

Simplifying
x = -2.9198698447


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3484412733, -2.9198698447}

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