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Simplifying 10X2 + -11X + -6 = 0 + 6 Reorder the terms: -6 + -11X + 10X2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6 + -11X + 10X2 = 6 Solving -6 + -11X + 10X2 = 6 Solving for variable 'X'. Reorder the terms: -6 + -6 + -11X + 10X2 = 6 + -6 Combine like terms: -6 + -6 = -12 -12 + -11X + 10X2 = 6 + -6 Combine like terms: 6 + -6 = 0 -12 + -11X + 10X2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + -1.1X + X2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.1X + 1.2 + X2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.1X + X2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.1X + X2 = 0 + 1.2 -1.1X + X2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.1X + X2 = 1.2 The X term is -1.1X. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1X + 0.3025 + X2 = 1.2 + 0.3025 Reorder the terms: 0.3025 + -1.1X + X2 = 1.2 + 0.3025 Combine like terms: 1.2 + 0.3025 = 1.5025 0.3025 + -1.1X + X2 = 1.5025 Factor a perfect square on the left side: (X + -0.55)(X + -0.55) = 1.5025 Calculate the square root of the right side: 1.225765067 Break this problem into two subproblems by setting (X + -0.55) equal to 1.225765067 and -1.225765067.Subproblem 1
X + -0.55 = 1.225765067 Simplifying X + -0.55 = 1.225765067 Reorder the terms: -0.55 + X = 1.225765067 Solving -0.55 + X = 1.225765067 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + X = 1.225765067 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + X = 1.225765067 + 0.55 X = 1.225765067 + 0.55 Combine like terms: 1.225765067 + 0.55 = 1.775765067 X = 1.775765067 Simplifying X = 1.775765067Subproblem 2
X + -0.55 = -1.225765067 Simplifying X + -0.55 = -1.225765067 Reorder the terms: -0.55 + X = -1.225765067 Solving -0.55 + X = -1.225765067 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + X = -1.225765067 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + X = -1.225765067 + 0.55 X = -1.225765067 + 0.55 Combine like terms: -1.225765067 + 0.55 = -0.675765067 X = -0.675765067 Simplifying X = -0.675765067Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.775765067, -0.675765067}
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