(3x-4)(3x-4)=23

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Solution for (3x-4)(3x-4)=23 equation:


Simplifying
(3x + -4)(3x + -4) = 23

Reorder the terms:
(-4 + 3x)(3x + -4) = 23

Reorder the terms:
(-4 + 3x)(-4 + 3x) = 23

Multiply (-4 + 3x) * (-4 + 3x)
(-4(-4 + 3x) + 3x * (-4 + 3x)) = 23
((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) = 23
((16 + -12x) + 3x * (-4 + 3x)) = 23
(16 + -12x + (-4 * 3x + 3x * 3x)) = 23
(16 + -12x + (-12x + 9x2)) = 23

Combine like terms: -12x + -12x = -24x
(16 + -24x + 9x2) = 23

Solving
16 + -24x + 9x2 = 23

Solving for variable 'x'.

Reorder the terms:
16 + -23 + -24x + 9x2 = 23 + -23

Combine like terms: 16 + -23 = -7
-7 + -24x + 9x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-7 + -24x + 9x2 = 0

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

Divide each side by '9'.
-0.7777777778 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -2.666666667x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -2.666666667x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + 0.7777777778
-2.666666667x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-2.666666667x + x2 = 0.7777777778

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 = 0.7777777778 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 0.7777777778 + 1.777777780

Combine like terms: 0.7777777778 + 1.777777780 = 2.5555555578
1.777777780 + -2.666666667x + x2 = 2.5555555578

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 2.5555555578

Calculate the square root of the right side: 1.598610508

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.598610508 and -1.598610508.

Subproblem 1

x + -1.333333334 = 1.598610508 Simplifying x + -1.333333334 = 1.598610508 Reorder the terms: -1.333333334 + x = 1.598610508 Solving -1.333333334 + x = 1.598610508 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 = 1.598610508 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.598610508 + 1.333333334 x = 1.598610508 + 1.333333334 Combine like terms: 1.598610508 + 1.333333334 = 2.931943842 x = 2.931943842 Simplifying x = 2.931943842

Subproblem 2

x + -1.333333334 = -1.598610508 Simplifying x + -1.333333334 = -1.598610508 Reorder the terms: -1.333333334 + x = -1.598610508 Solving -1.333333334 + x = -1.598610508 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 = -1.598610508 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.598610508 + 1.333333334 x = -1.598610508 + 1.333333334 Combine like terms: -1.598610508 + 1.333333334 = -0.265277174 x = -0.265277174 Simplifying x = -0.265277174

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.931943842, -0.265277174}

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