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Simplifying 14x2 + 45x + 51 = 0 Reorder the terms: 51 + 45x + 14x2 = 0 Solving 51 + 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'. 3.642857143 + 3.214285714x + x2 = 0 Move the constant term to the right: Add '-3.642857143' to each side of the equation. 3.642857143 + 3.214285714x + -3.642857143 + x2 = 0 + -3.642857143 Reorder the terms: 3.642857143 + -3.642857143 + 3.214285714x + x2 = 0 + -3.642857143 Combine like terms: 3.642857143 + -3.642857143 = 0.000000000 0.000000000 + 3.214285714x + x2 = 0 + -3.642857143 3.214285714x + x2 = 0 + -3.642857143 Combine like terms: 0 + -3.642857143 = -3.642857143 3.214285714x + x2 = -3.642857143 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 = -3.642857143 + 2.582908163 Reorder the terms: 2.582908163 + 3.214285714x + x2 = -3.642857143 + 2.582908163 Combine like terms: -3.642857143 + 2.582908163 = -1.05994898 2.582908163 + 3.214285714x + x2 = -1.05994898 Factor a perfect square on the left side: (x + 1.607142857)(x + 1.607142857) = -1.05994898 Can't calculate square root of the right side. The solution to this equation could not be determined.
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