3x(x-5)=1+5(x-6)

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Solution for 3x(x-5)=1+5(x-6) equation:


Simplifying
3x(x + -5) = 1 + 5(x + -6)

Reorder the terms:
3x(-5 + x) = 1 + 5(x + -6)
(-5 * 3x + x * 3x) = 1 + 5(x + -6)
(-15x + 3x2) = 1 + 5(x + -6)

Reorder the terms:
-15x + 3x2 = 1 + 5(-6 + x)
-15x + 3x2 = 1 + (-6 * 5 + x * 5)
-15x + 3x2 = 1 + (-30 + 5x)

Combine like terms: 1 + -30 = -29
-15x + 3x2 = -29 + 5x

Solving
-15x + 3x2 = -29 + 5x

Solving for variable 'x'.

Reorder the terms:
29 + -15x + -5x + 3x2 = -29 + 5x + 29 + -5x

Combine like terms: -15x + -5x = -20x
29 + -20x + 3x2 = -29 + 5x + 29 + -5x

Reorder the terms:
29 + -20x + 3x2 = -29 + 29 + 5x + -5x

Combine like terms: -29 + 29 = 0
29 + -20x + 3x2 = 0 + 5x + -5x
29 + -20x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
29 + -20x + 3x2 = 0

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

Divide each side by '3'.
9.666666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + -6.666666667x + -9.666666667 + x2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + -6.666666667x + x2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -9.666666667
-6.666666667x + x2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
-6.666666667x + x2 = -9.666666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -9.666666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -9.666666667 + 11.11111112

Combine like terms: -9.666666667 + 11.11111112 = 1.444444453
11.11111112 + -6.666666667x + x2 = 1.444444453

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 1.444444453

Calculate the square root of the right side: 1.201850429

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 1.201850429 and -1.201850429.

Subproblem 1

x + -3.333333334 = 1.201850429 Simplifying x + -3.333333334 = 1.201850429 Reorder the terms: -3.333333334 + x = 1.201850429 Solving -3.333333334 + x = 1.201850429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 1.201850429 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 1.201850429 + 3.333333334 x = 1.201850429 + 3.333333334 Combine like terms: 1.201850429 + 3.333333334 = 4.535183763 x = 4.535183763 Simplifying x = 4.535183763

Subproblem 2

x + -3.333333334 = -1.201850429 Simplifying x + -3.333333334 = -1.201850429 Reorder the terms: -3.333333334 + x = -1.201850429 Solving -3.333333334 + x = -1.201850429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -1.201850429 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -1.201850429 + 3.333333334 x = -1.201850429 + 3.333333334 Combine like terms: -1.201850429 + 3.333333334 = 2.131482905 x = 2.131482905 Simplifying x = 2.131482905

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.535183763, 2.131482905}

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