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Simplifying 20X2 + -23X + -6 = 0 Reorder the terms: -6 + -23X + 20X2 = 0 Solving -6 + -23X + 20X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.3 + -1.15X + X2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.15X + 0.3 + X2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.15X + X2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.15X + X2 = 0 + 0.3 -1.15X + X2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -1.15X + X2 = 0.3 The X term is -1.15X. Take half its coefficient (-0.575). Square it (0.330625) and add it to both sides. Add '0.330625' to each side of the equation. -1.15X + 0.330625 + X2 = 0.3 + 0.330625 Reorder the terms: 0.330625 + -1.15X + X2 = 0.3 + 0.330625 Combine like terms: 0.3 + 0.330625 = 0.630625 0.330625 + -1.15X + X2 = 0.630625 Factor a perfect square on the left side: (X + -0.575)(X + -0.575) = 0.630625 Calculate the square root of the right side: 0.794119009 Break this problem into two subproblems by setting (X + -0.575) equal to 0.794119009 and -0.794119009.Subproblem 1
X + -0.575 = 0.794119009 Simplifying X + -0.575 = 0.794119009 Reorder the terms: -0.575 + X = 0.794119009 Solving -0.575 + X = 0.794119009 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.575' to each side of the equation. -0.575 + 0.575 + X = 0.794119009 + 0.575 Combine like terms: -0.575 + 0.575 = 0.000 0.000 + X = 0.794119009 + 0.575 X = 0.794119009 + 0.575 Combine like terms: 0.794119009 + 0.575 = 1.369119009 X = 1.369119009 Simplifying X = 1.369119009Subproblem 2
X + -0.575 = -0.794119009 Simplifying X + -0.575 = -0.794119009 Reorder the terms: -0.575 + X = -0.794119009 Solving -0.575 + X = -0.794119009 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.575' to each side of the equation. -0.575 + 0.575 + X = -0.794119009 + 0.575 Combine like terms: -0.575 + 0.575 = 0.000 0.000 + X = -0.794119009 + 0.575 X = -0.794119009 + 0.575 Combine like terms: -0.794119009 + 0.575 = -0.219119009 X = -0.219119009 Simplifying X = -0.219119009Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.369119009, -0.219119009}
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