3x[3+2x(32-10)]=71

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Solution for 3x[3+2x(32-10)]=71 equation:


Simplifying
3x[3 + 2x(32 + -10)] = 71

Combine like terms: 32 + -10 = 22
3x[3 + 2x(22)] = 71

Reorder the terms for easier multiplication:
3x[3 + 2 * 22x] = 71

Multiply 2 * 22
3x[3 + 44x] = 71
[3 * 3x + 44x * 3x] = 71
[9x + 132x2] = 71

Solving
9x + 132x2 = 71

Solving for variable 'x'.

Reorder the terms:
-71 + 9x + 132x2 = 71 + -71

Combine like terms: 71 + -71 = 0
-71 + 9x + 132x2 = 0

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

Divide each side by '132'.
-0.5378787879 + 0.06818181818x + x2 = 0

Move the constant term to the right:

Add '0.5378787879' to each side of the equation.
-0.5378787879 + 0.06818181818x + 0.5378787879 + x2 = 0 + 0.5378787879

Reorder the terms:
-0.5378787879 + 0.5378787879 + 0.06818181818x + x2 = 0 + 0.5378787879

Combine like terms: -0.5378787879 + 0.5378787879 = 0.0000000000
0.0000000000 + 0.06818181818x + x2 = 0 + 0.5378787879
0.06818181818x + x2 = 0 + 0.5378787879

Combine like terms: 0 + 0.5378787879 = 0.5378787879
0.06818181818x + x2 = 0.5378787879

The x term is 0.06818181818x.  Take half its coefficient (0.03409090909).
Square it (0.001162190083) and add it to both sides.

Add '0.001162190083' to each side of the equation.
0.06818181818x + 0.001162190083 + x2 = 0.5378787879 + 0.001162190083

Reorder the terms:
0.001162190083 + 0.06818181818x + x2 = 0.5378787879 + 0.001162190083

Combine like terms: 0.5378787879 + 0.001162190083 = 0.539040977983
0.001162190083 + 0.06818181818x + x2 = 0.539040977983

Factor a perfect square on the left side:
(x + 0.03409090909)(x + 0.03409090909) = 0.539040977983

Calculate the square root of the right side: 0.734194101

Break this problem into two subproblems by setting 
(x + 0.03409090909) equal to 0.734194101 and -0.734194101.

Subproblem 1

x + 0.03409090909 = 0.734194101 Simplifying x + 0.03409090909 = 0.734194101 Reorder the terms: 0.03409090909 + x = 0.734194101 Solving 0.03409090909 + x = 0.734194101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03409090909' to each side of the equation. 0.03409090909 + -0.03409090909 + x = 0.734194101 + -0.03409090909 Combine like terms: 0.03409090909 + -0.03409090909 = 0.00000000000 0.00000000000 + x = 0.734194101 + -0.03409090909 x = 0.734194101 + -0.03409090909 Combine like terms: 0.734194101 + -0.03409090909 = 0.70010319191 x = 0.70010319191 Simplifying x = 0.70010319191

Subproblem 2

x + 0.03409090909 = -0.734194101 Simplifying x + 0.03409090909 = -0.734194101 Reorder the terms: 0.03409090909 + x = -0.734194101 Solving 0.03409090909 + x = -0.734194101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03409090909' to each side of the equation. 0.03409090909 + -0.03409090909 + x = -0.734194101 + -0.03409090909 Combine like terms: 0.03409090909 + -0.03409090909 = 0.00000000000 0.00000000000 + x = -0.734194101 + -0.03409090909 x = -0.734194101 + -0.03409090909 Combine like terms: -0.734194101 + -0.03409090909 = -0.76828501009 x = -0.76828501009 Simplifying x = -0.76828501009

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.70010319191, -0.76828501009}

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