123-45x^2-12x=0

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Solution for 123-45x^2-12x=0 equation:


Simplifying
123 + -45x2 + -12x = 0

Reorder the terms:
123 + -12x + -45x2 = 0

Solving
123 + -12x + -45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(41 + -4x + -15x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(41 + -4x + -15x2)' equal to zero and attempt to solve: Simplifying 41 + -4x + -15x2 = 0 Solving 41 + -4x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -2.733333333 + 0.2666666667x + x2 = 0 Move the constant term to the right: Add '2.733333333' to each side of the equation. -2.733333333 + 0.2666666667x + 2.733333333 + x2 = 0 + 2.733333333 Reorder the terms: -2.733333333 + 2.733333333 + 0.2666666667x + x2 = 0 + 2.733333333 Combine like terms: -2.733333333 + 2.733333333 = 0.000000000 0.000000000 + 0.2666666667x + x2 = 0 + 2.733333333 0.2666666667x + x2 = 0 + 2.733333333 Combine like terms: 0 + 2.733333333 = 2.733333333 0.2666666667x + x2 = 2.733333333 The x term is 0.2666666667x. Take half its coefficient (0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. 0.2666666667x + 0.01777777780 + x2 = 2.733333333 + 0.01777777780 Reorder the terms: 0.01777777780 + 0.2666666667x + x2 = 2.733333333 + 0.01777777780 Combine like terms: 2.733333333 + 0.01777777780 = 2.7511111108 0.01777777780 + 0.2666666667x + x2 = 2.7511111108 Factor a perfect square on the left side: (x + 0.1333333334)(x + 0.1333333334) = 2.7511111108 Calculate the square root of the right side: 1.658647374 Break this problem into two subproblems by setting (x + 0.1333333334) equal to 1.658647374 and -1.658647374.

Subproblem 1

x + 0.1333333334 = 1.658647374 Simplifying x + 0.1333333334 = 1.658647374 Reorder the terms: 0.1333333334 + x = 1.658647374 Solving 0.1333333334 + x = 1.658647374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = 1.658647374 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = 1.658647374 + -0.1333333334 x = 1.658647374 + -0.1333333334 Combine like terms: 1.658647374 + -0.1333333334 = 1.5253140406 x = 1.5253140406 Simplifying x = 1.5253140406

Subproblem 2

x + 0.1333333334 = -1.658647374 Simplifying x + 0.1333333334 = -1.658647374 Reorder the terms: 0.1333333334 + x = -1.658647374 Solving 0.1333333334 + x = -1.658647374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = -1.658647374 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = -1.658647374 + -0.1333333334 x = -1.658647374 + -0.1333333334 Combine like terms: -1.658647374 + -0.1333333334 = -1.7919807074 x = -1.7919807074 Simplifying x = -1.7919807074

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5253140406, -1.7919807074}

Solution

x = {1.5253140406, -1.7919807074}

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