x=(6x-10)(6x+10)

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Solution for x=(6x-10)(6x+10) equation:


Simplifying
x = (6x + -10)(6x + 10)

Reorder the terms:
x = (-10 + 6x)(6x + 10)

Reorder the terms:
x = (-10 + 6x)(10 + 6x)

Multiply (-10 + 6x) * (10 + 6x)
x = (-10(10 + 6x) + 6x * (10 + 6x))
x = ((10 * -10 + 6x * -10) + 6x * (10 + 6x))
x = ((-100 + -60x) + 6x * (10 + 6x))
x = (-100 + -60x + (10 * 6x + 6x * 6x))
x = (-100 + -60x + (60x + 36x2))

Combine like terms: -60x + 60x = 0
x = (-100 + 0 + 36x2)
x = (-100 + 36x2)

Solving
x = -100 + 36x2

Solving for variable 'x'.

Reorder the terms:
100 + x + -36x2 = -100 + 36x2 + 100 + -36x2

Reorder the terms:
100 + x + -36x2 = -100 + 100 + 36x2 + -36x2

Combine like terms: -100 + 100 = 0
100 + x + -36x2 = 0 + 36x2 + -36x2
100 + x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
100 + x + -36x2 = 0

Begin completing the square.  Divide all terms by
-36 the coefficient of the squared term: 

Divide each side by '-36'.
-2.777777778 + -0.02777777778x + x2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + -0.02777777778x + 2.777777778 + x2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + -0.02777777778x + x2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + -0.02777777778x + x2 = 0 + 2.777777778
-0.02777777778x + x2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
-0.02777777778x + x2 = 2.777777778

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.
-0.02777777778x + 0.25 + x2 = 2.777777778 + 0.25

Reorder the terms:
0.25 + -0.02777777778x + x2 = 2.777777778 + 0.25

Combine like terms: 2.777777778 + 0.25 = 3.027777778
0.25 + -0.02777777778x + x2 = 3.027777778

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.027777778

Calculate the square root of the right side: 1.740051085

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.740051085 and -1.740051085.

Subproblem 1

x + 0.5 = 1.740051085 Simplifying x + 0.5 = 1.740051085 Reorder the terms: 0.5 + x = 1.740051085 Solving 0.5 + x = 1.740051085 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 = 1.740051085 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.740051085 + -0.5 x = 1.740051085 + -0.5 Combine like terms: 1.740051085 + -0.5 = 1.240051085 x = 1.240051085 Simplifying x = 1.240051085

Subproblem 2

x + 0.5 = -1.740051085 Simplifying x + 0.5 = -1.740051085 Reorder the terms: 0.5 + x = -1.740051085 Solving 0.5 + x = -1.740051085 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 = -1.740051085 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.740051085 + -0.5 x = -1.740051085 + -0.5 Combine like terms: -1.740051085 + -0.5 = -2.240051085 x = -2.240051085 Simplifying x = -2.240051085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.240051085, -2.240051085}

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