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Simplifying 14x2 + -45x + -4 = 0 Reorder the terms: -4 + -45x + 14x2 = 0 Solving -4 + -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'. -0.2857142857 + -3.214285714x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -3.214285714x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -3.214285714x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -3.214285714x + x2 = 0 + 0.2857142857 -3.214285714x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -3.214285714x + x2 = 0.2857142857 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 = 0.2857142857 + 2.582908163 Reorder the terms: 2.582908163 + -3.214285714x + x2 = 0.2857142857 + 2.582908163 Combine like terms: 0.2857142857 + 2.582908163 = 2.8686224487 2.582908163 + -3.214285714x + x2 = 2.8686224487 Factor a perfect square on the left side: (x + -1.607142857)(x + -1.607142857) = 2.8686224487 Calculate the square root of the right side: 1.693700814 Break this problem into two subproblems by setting (x + -1.607142857) equal to 1.693700814 and -1.693700814.Subproblem 1
x + -1.607142857 = 1.693700814 Simplifying x + -1.607142857 = 1.693700814 Reorder the terms: -1.607142857 + x = 1.693700814 Solving -1.607142857 + x = 1.693700814 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 = 1.693700814 + 1.607142857 Combine like terms: -1.607142857 + 1.607142857 = 0.000000000 0.000000000 + x = 1.693700814 + 1.607142857 x = 1.693700814 + 1.607142857 Combine like terms: 1.693700814 + 1.607142857 = 3.300843671 x = 3.300843671 Simplifying x = 3.300843671Subproblem 2
x + -1.607142857 = -1.693700814 Simplifying x + -1.607142857 = -1.693700814 Reorder the terms: -1.607142857 + x = -1.693700814 Solving -1.607142857 + x = -1.693700814 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 = -1.693700814 + 1.607142857 Combine like terms: -1.607142857 + 1.607142857 = 0.000000000 0.000000000 + x = -1.693700814 + 1.607142857 x = -1.693700814 + 1.607142857 Combine like terms: -1.693700814 + 1.607142857 = -0.086557957 x = -0.086557957 Simplifying x = -0.086557957Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.300843671, -0.086557957}
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