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Simplifying -14x2 + -47x + -97 = 0 Reorder the terms: -97 + -47x + -14x2 = 0 Solving -97 + -47x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(97 + 47x + 14x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(97 + 47x + 14x2)' equal to zero and attempt to solve: Simplifying 97 + 47x + 14x2 = 0 Solving 97 + 47x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 6.928571429 + 3.357142857x + x2 = 0 Move the constant term to the right: Add '-6.928571429' to each side of the equation. 6.928571429 + 3.357142857x + -6.928571429 + x2 = 0 + -6.928571429 Reorder the terms: 6.928571429 + -6.928571429 + 3.357142857x + x2 = 0 + -6.928571429 Combine like terms: 6.928571429 + -6.928571429 = 0.000000000 0.000000000 + 3.357142857x + x2 = 0 + -6.928571429 3.357142857x + x2 = 0 + -6.928571429 Combine like terms: 0 + -6.928571429 = -6.928571429 3.357142857x + x2 = -6.928571429 The x term is 3.357142857x. Take half its coefficient (1.678571429). Square it (2.817602042) and add it to both sides. Add '2.817602042' to each side of the equation. 3.357142857x + 2.817602042 + x2 = -6.928571429 + 2.817602042 Reorder the terms: 2.817602042 + 3.357142857x + x2 = -6.928571429 + 2.817602042 Combine like terms: -6.928571429 + 2.817602042 = -4.110969387 2.817602042 + 3.357142857x + x2 = -4.110969387 Factor a perfect square on the left side: (x + 1.678571429)(x + 1.678571429) = -4.110969387 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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