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Simplifying 10X2 + -54X + 9 = 0 Reorder the terms: 9 + -54X + 10X2 = 0 Solving 9 + -54X + 10X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.9 + -5.4X + X2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -5.4X + -0.9 + X2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -5.4X + X2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -5.4X + X2 = 0 + -0.9 -5.4X + X2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -5.4X + X2 = -0.9 The X term is -5.4X. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4X + 7.29 + X2 = -0.9 + 7.29 Reorder the terms: 7.29 + -5.4X + X2 = -0.9 + 7.29 Combine like terms: -0.9 + 7.29 = 6.39 7.29 + -5.4X + X2 = 6.39 Factor a perfect square on the left side: (X + -2.7)(X + -2.7) = 6.39 Calculate the square root of the right side: 2.527844932 Break this problem into two subproblems by setting (X + -2.7) equal to 2.527844932 and -2.527844932.Subproblem 1
X + -2.7 = 2.527844932 Simplifying X + -2.7 = 2.527844932 Reorder the terms: -2.7 + X = 2.527844932 Solving -2.7 + X = 2.527844932 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + X = 2.527844932 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + X = 2.527844932 + 2.7 X = 2.527844932 + 2.7 Combine like terms: 2.527844932 + 2.7 = 5.227844932 X = 5.227844932 Simplifying X = 5.227844932Subproblem 2
X + -2.7 = -2.527844932 Simplifying X + -2.7 = -2.527844932 Reorder the terms: -2.7 + X = -2.527844932 Solving -2.7 + X = -2.527844932 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + X = -2.527844932 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + X = -2.527844932 + 2.7 X = -2.527844932 + 2.7 Combine like terms: -2.527844932 + 2.7 = 0.172155068 X = 0.172155068 Simplifying X = 0.172155068Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.227844932, 0.172155068}
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