(3x^2)-(25x)-(28)=x

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Solution for (3x^2)-(25x)-(28)=x equation:


Simplifying
(3x2) + -1(25x) + -1(28) = x

Remove parenthesis around (25x)
(3x2) + -1 * 25x + -1(28) = x

Multiply -1 * 25
(3x2) + -25x + -1(28) = x

Multiply -1 * 28
(3x2) + -25x + -28 = x

Reorder the terms:
-28 + -25x + (3x2) = x

Solving
-28 + -25x + (3x2) = x

Solving for variable 'x'.

Reorder the terms:
-28 + -25x + -1x + (3x2) = x + -1x

Combine like terms: -25x + -1x = -26x
-28 + -26x + (3x2) = x + -1x

Combine like terms: x + -1x = 0
-28 + -26x + (3x2) = 0

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

Divide each side by '3'.
-9.333333333 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -8.666666667x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -8.666666667x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -8.666666667x + x2 = 0 + 9.333333333
-8.666666667x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-8.666666667x + x2 = 9.333333333

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = 9.333333333 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = 9.333333333 + 18.77777778

Combine like terms: 9.333333333 + 18.77777778 = 28.111111113
18.77777778 + -8.666666667x + x2 = 28.111111113

Factor a perfect square on the left side:
((x) + -4.333333334)((x) + -4.333333334) = 28.111111113

Calculate the square root of the right side: 5.30199124

Break this problem into two subproblems by setting 
((x) + -4.333333334) equal to 5.30199124 and -5.30199124.

Subproblem 1

(x) + -4.333333334 = 5.30199124 Simplifying (x) + -4.333333334 = 5.30199124 x + -4.333333334 = 5.30199124 Reorder the terms: -4.333333334 + x = 5.30199124 Solving -4.333333334 + x = 5.30199124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 5.30199124 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 5.30199124 + 4.333333334 x = 5.30199124 + 4.333333334 Combine like terms: 5.30199124 + 4.333333334 = 9.635324574 x = 9.635324574 Simplifying x = 9.635324574

Subproblem 2

(x) + -4.333333334 = -5.30199124 Simplifying (x) + -4.333333334 = -5.30199124 x + -4.333333334 = -5.30199124 Reorder the terms: -4.333333334 + x = -5.30199124 Solving -4.333333334 + x = -5.30199124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -5.30199124 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -5.30199124 + 4.333333334 x = -5.30199124 + 4.333333334 Combine like terms: -5.30199124 + 4.333333334 = -0.968657906 x = -0.968657906 Simplifying x = -0.968657906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.635324574, -0.968657906}

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