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Simplifying 12x2 + -58x + -22 = 0 Reorder the terms: -22 + -58x + 12x2 = 0 Solving -22 + -58x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + -29x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -29x + 6x2)' equal to zero and attempt to solve: Simplifying -11 + -29x + 6x2 = 0 Solving -11 + -29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -4.833333333x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -4.833333333x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -4.833333333x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -4.833333333x + x2 = 0 + 1.833333333 -4.833333333x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -4.833333333x + x2 = 1.833333333 The x term is -4.833333333x. Take half its coefficient (-2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. -4.833333333x + 5.840277779 + x2 = 1.833333333 + 5.840277779 Reorder the terms: 5.840277779 + -4.833333333x + x2 = 1.833333333 + 5.840277779 Combine like terms: 1.833333333 + 5.840277779 = 7.673611112 5.840277779 + -4.833333333x + x2 = 7.673611112 Factor a perfect square on the left side: (x + -2.416666667)(x + -2.416666667) = 7.673611112 Calculate the square root of the right side: 2.770128357 Break this problem into two subproblems by setting (x + -2.416666667) equal to 2.770128357 and -2.770128357.Subproblem 1
x + -2.416666667 = 2.770128357 Simplifying x + -2.416666667 = 2.770128357 Reorder the terms: -2.416666667 + x = 2.770128357 Solving -2.416666667 + x = 2.770128357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = 2.770128357 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = 2.770128357 + 2.416666667 x = 2.770128357 + 2.416666667 Combine like terms: 2.770128357 + 2.416666667 = 5.186795024 x = 5.186795024 Simplifying x = 5.186795024Subproblem 2
x + -2.416666667 = -2.770128357 Simplifying x + -2.416666667 = -2.770128357 Reorder the terms: -2.416666667 + x = -2.770128357 Solving -2.416666667 + x = -2.770128357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = -2.770128357 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = -2.770128357 + 2.416666667 x = -2.770128357 + 2.416666667 Combine like terms: -2.770128357 + 2.416666667 = -0.35346169 x = -0.35346169 Simplifying x = -0.35346169Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.186795024, -0.35346169}Solution
x = {5.186795024, -0.35346169}
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