(3x+8)(x)=100

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Solution for (3x+8)(x)=100 equation:


Simplifying
(3x + 8)(x) = 100

Reorder the terms:
(8 + 3x)(x) = 100

Reorder the terms for easier multiplication:
x(8 + 3x) = 100
(8 * x + 3x * x) = 100
(8x + 3x2) = 100

Solving
8x + 3x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 8x + 3x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 8x + 3x2 = 0

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

Divide each side by '3'.
-33.33333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + 2.666666667x + 33.33333333 + x2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + 2.666666667x + x2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 33.33333333
2.666666667x + x2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
2.666666667x + x2 = 33.33333333

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 33.33333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 33.33333333 + 1.777777780

Combine like terms: 33.33333333 + 1.777777780 = 35.11111111
1.777777780 + 2.666666667x + x2 = 35.11111111

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 35.11111111

Calculate the square root of the right side: 5.925462945

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 5.925462945 and -5.925462945.

Subproblem 1

x + 1.333333334 = 5.925462945 Simplifying x + 1.333333334 = 5.925462945 Reorder the terms: 1.333333334 + x = 5.925462945 Solving 1.333333334 + x = 5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 5.925462945 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.925462945 + -1.333333334 x = 5.925462945 + -1.333333334 Combine like terms: 5.925462945 + -1.333333334 = 4.592129611 x = 4.592129611 Simplifying x = 4.592129611

Subproblem 2

x + 1.333333334 = -5.925462945 Simplifying x + 1.333333334 = -5.925462945 Reorder the terms: 1.333333334 + x = -5.925462945 Solving 1.333333334 + x = -5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -5.925462945 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.925462945 + -1.333333334 x = -5.925462945 + -1.333333334 Combine like terms: -5.925462945 + -1.333333334 = -7.258796279 x = -7.258796279 Simplifying x = -7.258796279

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.592129611, -7.258796279}

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