2x^2-12x+5=9

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Solution for 2x^2-12x+5=9 equation:


Simplifying
2x2 + -12x + 5 = 9

Reorder the terms:
5 + -12x + 2x2 = 9

Solving
5 + -12x + 2x2 = 9

Solving for variable 'x'.

Reorder the terms:
5 + -9 + -12x + 2x2 = 9 + -9

Combine like terms: 5 + -9 = -4
-4 + -12x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-4 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -6x + x2)' equal to zero and attempt to solve: Simplifying -2 + -6x + x2 = 0 Solving -2 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6x + x2 = 0 + 2 -6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6x + x2 = 2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + -6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6x + x2 = 11 Factor a perfect square on the left side: (x + -3)(x + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -3) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -3 = 3.31662479 Simplifying x + -3 = 3.31662479 Reorder the terms: -3 + x = 3.31662479 Solving -3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.31662479 + 3 x = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 x = 6.31662479 Simplifying x = 6.31662479

Subproblem 2

x + -3 = -3.31662479 Simplifying x + -3 = -3.31662479 Reorder the terms: -3 + x = -3.31662479 Solving -3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.31662479 + 3 x = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 x = -0.31662479 Simplifying x = -0.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.31662479, -0.31662479}

Solution

x = {6.31662479, -0.31662479}

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