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Simplifying 14x2 + 60x + 25 = 0 Reorder the terms: 25 + 60x + 14x2 = 0 Solving 25 + 60x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.785714286 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '-1.785714286' to each side of the equation. 1.785714286 + 4.285714286x + -1.785714286 + x2 = 0 + -1.785714286 Reorder the terms: 1.785714286 + -1.785714286 + 4.285714286x + x2 = 0 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + 4.285714286x + x2 = 0 + -1.785714286 4.285714286x + x2 = 0 + -1.785714286 Combine like terms: 0 + -1.785714286 = -1.785714286 4.285714286x + x2 = -1.785714286 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = -1.785714286 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = -1.785714286 + 4.591836735 Combine like terms: -1.785714286 + 4.591836735 = 2.806122449 4.591836735 + 4.285714286x + x2 = 2.806122449 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = 2.806122449 Calculate the square root of the right side: 1.675148486 Break this problem into two subproblems by setting (x + 2.142857143) equal to 1.675148486 and -1.675148486.Subproblem 1
x + 2.142857143 = 1.675148486 Simplifying x + 2.142857143 = 1.675148486 Reorder the terms: 2.142857143 + x = 1.675148486 Solving 2.142857143 + x = 1.675148486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = 1.675148486 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = 1.675148486 + -2.142857143 x = 1.675148486 + -2.142857143 Combine like terms: 1.675148486 + -2.142857143 = -0.467708657 x = -0.467708657 Simplifying x = -0.467708657Subproblem 2
x + 2.142857143 = -1.675148486 Simplifying x + 2.142857143 = -1.675148486 Reorder the terms: 2.142857143 + x = -1.675148486 Solving 2.142857143 + x = -1.675148486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = -1.675148486 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = -1.675148486 + -2.142857143 x = -1.675148486 + -2.142857143 Combine like terms: -1.675148486 + -2.142857143 = -3.818005629 x = -3.818005629 Simplifying x = -3.818005629Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.467708657, -3.818005629}
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