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Simplifying 2x2 + -12x + -104 = 0 Reorder the terms: -104 + -12x + 2x2 = 0 Solving -104 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + -6x + x2)' equal to zero and attempt to solve: Simplifying -52 + -6x + x2 = 0 Solving -52 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -6x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -6x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -6x + x2 = 0 + 52 -6x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -6x + x2 = 52 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 = 52 + 9 Reorder the terms: 9 + -6x + x2 = 52 + 9 Combine like terms: 52 + 9 = 61 9 + -6x + x2 = 61 Factor a perfect square on the left side: (x + -3)(x + -3) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -3) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -3 = 7.810249676 Simplifying x + -3 = 7.810249676 Reorder the terms: -3 + x = 7.810249676 Solving -3 + x = 7.810249676 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 = 7.810249676 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.810249676 + 3 x = 7.810249676 + 3 Combine like terms: 7.810249676 + 3 = 10.810249676 x = 10.810249676 Simplifying x = 10.810249676Subproblem 2
x + -3 = -7.810249676 Simplifying x + -3 = -7.810249676 Reorder the terms: -3 + x = -7.810249676 Solving -3 + x = -7.810249676 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 = -7.810249676 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.810249676 + 3 x = -7.810249676 + 3 Combine like terms: -7.810249676 + 3 = -4.810249676 x = -4.810249676 Simplifying x = -4.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.810249676, -4.810249676}Solution
x = {10.810249676, -4.810249676}
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