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Simplifying 14x2 + 45x + -22 = 0 Reorder the terms: -22 + 45x + 14x2 = 0 Solving -22 + 45x + 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'. -1.571428571 + 3.214285714x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 3.214285714x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 3.214285714x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 3.214285714x + x2 = 0 + 1.571428571 3.214285714x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 3.214285714x + x2 = 1.571428571 The x term is 3.214285714x. Take half its coefficient (1.607142857). Square it (2.582908163) and add it to both sides. Add '2.582908163' to each side of the equation. 3.214285714x + 2.582908163 + x2 = 1.571428571 + 2.582908163 Reorder the terms: 2.582908163 + 3.214285714x + x2 = 1.571428571 + 2.582908163 Combine like terms: 1.571428571 + 2.582908163 = 4.154336734 2.582908163 + 3.214285714x + x2 = 4.154336734 Factor a perfect square on the left side: (x + 1.607142857)(x + 1.607142857) = 4.154336734 Calculate the square root of the right side: 2.03821901 Break this problem into two subproblems by setting (x + 1.607142857) equal to 2.03821901 and -2.03821901.Subproblem 1
x + 1.607142857 = 2.03821901 Simplifying x + 1.607142857 = 2.03821901 Reorder the terms: 1.607142857 + x = 2.03821901 Solving 1.607142857 + x = 2.03821901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.607142857' to each side of the equation. 1.607142857 + -1.607142857 + x = 2.03821901 + -1.607142857 Combine like terms: 1.607142857 + -1.607142857 = 0.000000000 0.000000000 + x = 2.03821901 + -1.607142857 x = 2.03821901 + -1.607142857 Combine like terms: 2.03821901 + -1.607142857 = 0.431076153 x = 0.431076153 Simplifying x = 0.431076153Subproblem 2
x + 1.607142857 = -2.03821901 Simplifying x + 1.607142857 = -2.03821901 Reorder the terms: 1.607142857 + x = -2.03821901 Solving 1.607142857 + x = -2.03821901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.607142857' to each side of the equation. 1.607142857 + -1.607142857 + x = -2.03821901 + -1.607142857 Combine like terms: 1.607142857 + -1.607142857 = 0.000000000 0.000000000 + x = -2.03821901 + -1.607142857 x = -2.03821901 + -1.607142857 Combine like terms: -2.03821901 + -1.607142857 = -3.645361867 x = -3.645361867 Simplifying x = -3.645361867Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.431076153, -3.645361867}
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