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Simplifying 5x2 + x + 25x + 25 = 0 Reorder the terms: 25 + x + 25x + 5x2 = 0 Combine like terms: x + 25x = 26x 25 + 26x + 5x2 = 0 Solving 25 + 26x + 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'. 5 + 5.2x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5.2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.2x + x2 = 0 + -5 5.2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.2x + x2 = -5 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = -5 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = -5 + 6.76 Combine like terms: -5 + 6.76 = 1.76 6.76 + 5.2x + x2 = 1.76 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + 2.6) equal to 1.326649916 and -1.326649916.Subproblem 1
x + 2.6 = 1.326649916 Simplifying x + 2.6 = 1.326649916 Reorder the terms: 2.6 + x = 1.326649916 Solving 2.6 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 1.326649916 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 1.326649916 + -2.6 x = 1.326649916 + -2.6 Combine like terms: 1.326649916 + -2.6 = -1.273350084 x = -1.273350084 Simplifying x = -1.273350084Subproblem 2
x + 2.6 = -1.326649916 Simplifying x + 2.6 = -1.326649916 Reorder the terms: 2.6 + x = -1.326649916 Solving 2.6 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -1.326649916 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -1.326649916 + -2.6 x = -1.326649916 + -2.6 Combine like terms: -1.326649916 + -2.6 = -3.926649916 x = -3.926649916 Simplifying x = -3.926649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.273350084, -3.926649916}
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