12x^2-42x+25=0

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Solution for 12x^2-42x+25=0 equation:


Simplifying
12x2 + -42x + 25 = 0

Reorder the terms:
25 + -42x + 12x2 = 0

Solving
25 + -42x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
2.083333333 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -3.5x + -2.083333333 + x2 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -3.5x + x2 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -3.5x + x2 = 0 + -2.083333333
-3.5x + x2 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-3.5x + x2 = -2.083333333

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2.083333333 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2.083333333 + 3.0625

Combine like terms: -2.083333333 + 3.0625 = 0.979166667
3.0625 + -3.5x + x2 = 0.979166667

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 0.979166667

Calculate the square root of the right side: 0.989528507

Break this problem into two subproblems by setting 
(x + -1.75) equal to 0.989528507 and -0.989528507.

Subproblem 1

x + -1.75 = 0.989528507 Simplifying x + -1.75 = 0.989528507 Reorder the terms: -1.75 + x = 0.989528507 Solving -1.75 + x = 0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 0.989528507 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.989528507 + 1.75 x = 0.989528507 + 1.75 Combine like terms: 0.989528507 + 1.75 = 2.739528507 x = 2.739528507 Simplifying x = 2.739528507

Subproblem 2

x + -1.75 = -0.989528507 Simplifying x + -1.75 = -0.989528507 Reorder the terms: -1.75 + x = -0.989528507 Solving -1.75 + x = -0.989528507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -0.989528507 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -0.989528507 + 1.75 x = -0.989528507 + 1.75 Combine like terms: -0.989528507 + 1.75 = 0.760471493 x = 0.760471493 Simplifying x = 0.760471493

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.739528507, 0.760471493}

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