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Simplifying 3X2 + -180X + 100 = 0 Reorder the terms: 100 + -180X + 3X2 = 0 Solving 100 + -180X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 33.33333333 + -60X + X2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + -60X + -33.33333333 + X2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + -60X + X2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + -60X + X2 = 0 + -33.33333333 -60X + X2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 -60X + X2 = -33.33333333 The X term is -60X. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60X + 900 + X2 = -33.33333333 + 900 Reorder the terms: 900 + -60X + X2 = -33.33333333 + 900 Combine like terms: -33.33333333 + 900 = 866.66666667 900 + -60X + X2 = 866.66666667 Factor a perfect square on the left side: (X + -30)(X + -30) = 866.66666667 Calculate the square root of the right side: 29.439202888 Break this problem into two subproblems by setting (X + -30) equal to 29.439202888 and -29.439202888.Subproblem 1
X + -30 = 29.439202888 Simplifying X + -30 = 29.439202888 Reorder the terms: -30 + X = 29.439202888 Solving -30 + X = 29.439202888 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + X = 29.439202888 + 30 Combine like terms: -30 + 30 = 0 0 + X = 29.439202888 + 30 X = 29.439202888 + 30 Combine like terms: 29.439202888 + 30 = 59.439202888 X = 59.439202888 Simplifying X = 59.439202888Subproblem 2
X + -30 = -29.439202888 Simplifying X + -30 = -29.439202888 Reorder the terms: -30 + X = -29.439202888 Solving -30 + X = -29.439202888 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + X = -29.439202888 + 30 Combine like terms: -30 + 30 = 0 0 + X = -29.439202888 + 30 X = -29.439202888 + 30 Combine like terms: -29.439202888 + 30 = 0.560797112 X = 0.560797112 Simplifying X = 0.560797112Solution
The solution to the problem is based on the solutions from the subproblems. X = {59.439202888, 0.560797112}
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