-396x^2+636x-126=0

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Solution for -396x^2+636x-126=0 equation:


Simplifying
-396x2 + 636x + -126 = 0

Reorder the terms:
-126 + 636x + -396x2 = 0

Solving
-126 + 636x + -396x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 106x + -66x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-21 + 106x + -66x2)' equal to zero and attempt to solve: Simplifying -21 + 106x + -66x2 = 0 Solving -21 + 106x + -66x2 = 0 Begin completing the square. Divide all terms by -66 the coefficient of the squared term: Divide each side by '-66'. 0.3181818182 + -1.606060606x + x2 = 0 Move the constant term to the right: Add '-0.3181818182' to each side of the equation. 0.3181818182 + -1.606060606x + -0.3181818182 + x2 = 0 + -0.3181818182 Reorder the terms: 0.3181818182 + -0.3181818182 + -1.606060606x + x2 = 0 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + -1.606060606x + x2 = 0 + -0.3181818182 -1.606060606x + x2 = 0 + -0.3181818182 Combine like terms: 0 + -0.3181818182 = -0.3181818182 -1.606060606x + x2 = -0.3181818182 The x term is -1.606060606x. Take half its coefficient (-0.803030303). Square it (0.6448576675) and add it to both sides. Add '0.6448576675' to each side of the equation. -1.606060606x + 0.6448576675 + x2 = -0.3181818182 + 0.6448576675 Reorder the terms: 0.6448576675 + -1.606060606x + x2 = -0.3181818182 + 0.6448576675 Combine like terms: -0.3181818182 + 0.6448576675 = 0.3266758493 0.6448576675 + -1.606060606x + x2 = 0.3266758493 Factor a perfect square on the left side: (x + -0.803030303)(x + -0.803030303) = 0.3266758493 Calculate the square root of the right side: 0.57155564 Break this problem into two subproblems by setting (x + -0.803030303) equal to 0.57155564 and -0.57155564.

Subproblem 1

x + -0.803030303 = 0.57155564 Simplifying x + -0.803030303 = 0.57155564 Reorder the terms: -0.803030303 + x = 0.57155564 Solving -0.803030303 + x = 0.57155564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.803030303' to each side of the equation. -0.803030303 + 0.803030303 + x = 0.57155564 + 0.803030303 Combine like terms: -0.803030303 + 0.803030303 = 0.000000000 0.000000000 + x = 0.57155564 + 0.803030303 x = 0.57155564 + 0.803030303 Combine like terms: 0.57155564 + 0.803030303 = 1.374585943 x = 1.374585943 Simplifying x = 1.374585943

Subproblem 2

x + -0.803030303 = -0.57155564 Simplifying x + -0.803030303 = -0.57155564 Reorder the terms: -0.803030303 + x = -0.57155564 Solving -0.803030303 + x = -0.57155564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.803030303' to each side of the equation. -0.803030303 + 0.803030303 + x = -0.57155564 + 0.803030303 Combine like terms: -0.803030303 + 0.803030303 = 0.000000000 0.000000000 + x = -0.57155564 + 0.803030303 x = -0.57155564 + 0.803030303 Combine like terms: -0.57155564 + 0.803030303 = 0.231474663 x = 0.231474663 Simplifying x = 0.231474663

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.374585943, 0.231474663}

Solution

x = {1.374585943, 0.231474663}

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