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Simplifying 12x2 + 4 + -5x + -7x2 + -11x = 0 Reorder the terms: 4 + -5x + -11x + 12x2 + -7x2 = 0 Combine like terms: -5x + -11x = -16x 4 + -16x + 12x2 + -7x2 = 0 Combine like terms: 12x2 + -7x2 = 5x2 4 + -16x + 5x2 = 0 Solving 4 + -16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -3.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -3.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -3.2x + x2 = 0 + -0.8 -3.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -3.2x + x2 = -0.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -0.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -0.8 + 2.56 Combine like terms: -0.8 + 2.56 = 1.76 2.56 + -3.2x + x2 = 1.76 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -1.6) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -1.6 = 1.326649916 Simplifying x + -1.6 = 1.326649916 Reorder the terms: -1.6 + x = 1.326649916 Solving -1.6 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.326649916 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.326649916 + 1.6 x = 1.326649916 + 1.6 Combine like terms: 1.326649916 + 1.6 = 2.926649916 x = 2.926649916 Simplifying x = 2.926649916Subproblem 2
x + -1.6 = -1.326649916 Simplifying x + -1.6 = -1.326649916 Reorder the terms: -1.6 + x = -1.326649916 Solving -1.6 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.326649916 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.326649916 + 1.6 x = -1.326649916 + 1.6 Combine like terms: -1.326649916 + 1.6 = 0.273350084 x = 0.273350084 Simplifying x = 0.273350084Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.926649916, 0.273350084}
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