6x*6x+17x-3=0

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Solution for 6x*6x+17x-3=0 equation:


Simplifying
6x * 6x + 17x + -3 = 0

Reorder the terms for easier multiplication:
6 * 6x * x + 17x + -3 = 0

Multiply 6 * 6
36x * x + 17x + -3 = 0

Multiply x * x
36x2 + 17x + -3 = 0

Reorder the terms:
-3 + 17x + 36x2 = 0

Solving
-3 + 17x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-0.08333333333 + 0.4722222222x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.4722222222x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.4722222222x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.4722222222x + x2 = 0 + 0.08333333333
0.4722222222x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
0.4722222222x + x2 = 0.08333333333

The x term is 0.4722222222x.  Take half its coefficient (0.2361111111).
Square it (0.05574845678) and add it to both sides.

Add '0.05574845678' to each side of the equation.
0.4722222222x + 0.05574845678 + x2 = 0.08333333333 + 0.05574845678

Reorder the terms:
0.05574845678 + 0.4722222222x + x2 = 0.08333333333 + 0.05574845678

Combine like terms: 0.08333333333 + 0.05574845678 = 0.13908179011
0.05574845678 + 0.4722222222x + x2 = 0.13908179011

Factor a perfect square on the left side:
(x + 0.2361111111)(x + 0.2361111111) = 0.13908179011

Calculate the square root of the right side: 0.372936711

Break this problem into two subproblems by setting 
(x + 0.2361111111) equal to 0.372936711 and -0.372936711.

Subproblem 1

x + 0.2361111111 = 0.372936711 Simplifying x + 0.2361111111 = 0.372936711 Reorder the terms: 0.2361111111 + x = 0.372936711 Solving 0.2361111111 + x = 0.372936711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2361111111' to each side of the equation. 0.2361111111 + -0.2361111111 + x = 0.372936711 + -0.2361111111 Combine like terms: 0.2361111111 + -0.2361111111 = 0.0000000000 0.0000000000 + x = 0.372936711 + -0.2361111111 x = 0.372936711 + -0.2361111111 Combine like terms: 0.372936711 + -0.2361111111 = 0.1368255999 x = 0.1368255999 Simplifying x = 0.1368255999

Subproblem 2

x + 0.2361111111 = -0.372936711 Simplifying x + 0.2361111111 = -0.372936711 Reorder the terms: 0.2361111111 + x = -0.372936711 Solving 0.2361111111 + x = -0.372936711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2361111111' to each side of the equation. 0.2361111111 + -0.2361111111 + x = -0.372936711 + -0.2361111111 Combine like terms: 0.2361111111 + -0.2361111111 = 0.0000000000 0.0000000000 + x = -0.372936711 + -0.2361111111 x = -0.372936711 + -0.2361111111 Combine like terms: -0.372936711 + -0.2361111111 = -0.6090478221 x = -0.6090478221 Simplifying x = -0.6090478221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1368255999, -0.6090478221}

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