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Simplifying 0.6x2 + -7.2x + 2 = 0 Reorder the terms: 2 + -7.2x + 0.6x2 = 0 Solving 2 + -7.2x + 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'. 3.333333333 + -12x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -12x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -12x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -12x + x2 = 0 + -3.333333333 -12x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -12x + x2 = -3.333333333 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -3.333333333 + 36 Reorder the terms: 36 + -12x + x2 = -3.333333333 + 36 Combine like terms: -3.333333333 + 36 = 32.666666667 36 + -12x + x2 = 32.666666667 Factor a perfect square on the left side: (x + -6)(x + -6) = 32.666666667 Calculate the square root of the right side: 5.715476067 Break this problem into two subproblems by setting (x + -6) equal to 5.715476067 and -5.715476067.Subproblem 1
x + -6 = 5.715476067 Simplifying x + -6 = 5.715476067 Reorder the terms: -6 + x = 5.715476067 Solving -6 + x = 5.715476067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.715476067 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.715476067 + 6 x = 5.715476067 + 6 Combine like terms: 5.715476067 + 6 = 11.715476067 x = 11.715476067 Simplifying x = 11.715476067Subproblem 2
x + -6 = -5.715476067 Simplifying x + -6 = -5.715476067 Reorder the terms: -6 + x = -5.715476067 Solving -6 + x = -5.715476067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.715476067 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.715476067 + 6 x = -5.715476067 + 6 Combine like terms: -5.715476067 + 6 = 0.284523933 x = 0.284523933 Simplifying x = 0.284523933Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.715476067, 0.284523933}
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