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Simplifying (5x2) + (14x) + 1 = 0 Reorder the terms: 1 + (14x) + (5x2) = 0 Solving 1 + (14x) + (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'. 0.2 + (2.8x) + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + (2.8x) + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + (2.8x) + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + (2.8x) + x2 = 0 + -0.2 (2.8x) + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 (2.8x) + x2 = -0.2 The x term is (2.8x). Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. (2.8x) + 1.96 + x2 = -0.2 + 1.96 Reorder the terms: 1.96 + (2.8x) + x2 = -0.2 + 1.96 Combine like terms: -0.2 + 1.96 = 1.76 1.96 + (2.8x) + x2 = 1.76 Factor a perfect square on the left side: ((x) + 1.4)((x) + 1.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting ((x) + 1.4) equal to 1.326649916 and -1.326649916.Subproblem 1
(x) + 1.4 = 1.326649916 Simplifying (x) + 1.4 = 1.326649916 x + 1.4 = 1.326649916 Reorder the terms: 1.4 + x = 1.326649916 Solving 1.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.326649916 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.326649916 + -1.4 x = 1.326649916 + -1.4 Combine like terms: 1.326649916 + -1.4 = -0.073350084 x = -0.073350084 Simplifying x = -0.073350084Subproblem 2
(x) + 1.4 = -1.326649916 Simplifying (x) + 1.4 = -1.326649916 x + 1.4 = -1.326649916 Reorder the terms: 1.4 + x = -1.326649916 Solving 1.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.326649916 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.326649916 + -1.4 x = -1.326649916 + -1.4 Combine like terms: -1.326649916 + -1.4 = -2.726649916 x = -2.726649916 Simplifying x = -2.726649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.073350084, -2.726649916}
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