(3x+3)(x)=77

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Solution for (3x+3)(x)=77 equation:


Simplifying
(3x + 3)(x) = 77

Reorder the terms:
(3 + 3x)(x) = 77

Reorder the terms for easier multiplication:
x(3 + 3x) = 77
(3 * x + 3x * x) = 77
(3x + 3x2) = 77

Solving
3x + 3x2 = 77

Solving for variable 'x'.

Reorder the terms:
-77 + 3x + 3x2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 3x + 3x2 = 0

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

Divide each side by '3'.
-25.66666667 + x + x2 = 0

Move the constant term to the right:

Add '25.66666667' to each side of the equation.
-25.66666667 + x + 25.66666667 + x2 = 0 + 25.66666667

Reorder the terms:
-25.66666667 + 25.66666667 + x + x2 = 0 + 25.66666667

Combine like terms: -25.66666667 + 25.66666667 = 0.00000000
0.00000000 + x + x2 = 0 + 25.66666667
x + x2 = 0 + 25.66666667

Combine like terms: 0 + 25.66666667 = 25.66666667
x + x2 = 25.66666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 25.66666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 25.66666667 + 0.25

Combine like terms: 25.66666667 + 0.25 = 25.91666667
1.25 + x2 = 25.91666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 25.91666667

Calculate the square root of the right side: 5.09084145

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.09084145 and -5.09084145.

Subproblem 1

x + 0.5 = 5.09084145 Simplifying x + 0.5 = 5.09084145 Reorder the terms: 0.5 + x = 5.09084145 Solving 0.5 + x = 5.09084145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.09084145 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.09084145 + -0.5 x = 5.09084145 + -0.5 Combine like terms: 5.09084145 + -0.5 = 4.59084145 x = 4.59084145 Simplifying x = 4.59084145

Subproblem 2

x + 0.5 = -5.09084145 Simplifying x + 0.5 = -5.09084145 Reorder the terms: 0.5 + x = -5.09084145 Solving 0.5 + x = -5.09084145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.09084145 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.09084145 + -0.5 x = -5.09084145 + -0.5 Combine like terms: -5.09084145 + -0.5 = -5.59084145 x = -5.59084145 Simplifying x = -5.59084145

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.59084145, -5.59084145}

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