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Simplifying 0.6x2 + -12x + 44 = 0 Reorder the terms: 44 + -12x + 0.6x2 = 0 Solving 44 + -12x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 73.33333333 + -20x + x2 = 0 Move the constant term to the right: Add '-73.33333333' to each side of the equation. 73.33333333 + -20x + -73.33333333 + x2 = 0 + -73.33333333 Reorder the terms: 73.33333333 + -73.33333333 + -20x + x2 = 0 + -73.33333333 Combine like terms: 73.33333333 + -73.33333333 = 0.00000000 0.00000000 + -20x + x2 = 0 + -73.33333333 -20x + x2 = 0 + -73.33333333 Combine like terms: 0 + -73.33333333 = -73.33333333 -20x + x2 = -73.33333333 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -73.33333333 + 100 Reorder the terms: 100 + -20x + x2 = -73.33333333 + 100 Combine like terms: -73.33333333 + 100 = 26.66666667 100 + -20x + x2 = 26.66666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 26.66666667 Calculate the square root of the right side: 5.163977795 Break this problem into two subproblems by setting (x + -10) equal to 5.163977795 and -5.163977795.Subproblem 1
x + -10 = 5.163977795 Simplifying x + -10 = 5.163977795 Reorder the terms: -10 + x = 5.163977795 Solving -10 + x = 5.163977795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.163977795 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.163977795 + 10 x = 5.163977795 + 10 Combine like terms: 5.163977795 + 10 = 15.163977795 x = 15.163977795 Simplifying x = 15.163977795Subproblem 2
x + -10 = -5.163977795 Simplifying x + -10 = -5.163977795 Reorder the terms: -10 + x = -5.163977795 Solving -10 + x = -5.163977795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.163977795 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.163977795 + 10 x = -5.163977795 + 10 Combine like terms: -5.163977795 + 10 = 4.836022205 x = 4.836022205 Simplifying x = 4.836022205Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.163977795, 4.836022205}
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