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Simplifying 9x * 8x + 2x = -114 Reorder the terms for easier multiplication: 9 * 8x * x + 2x = -114 Multiply 9 * 8 72x * x + 2x = -114 Multiply x * x 72x2 + 2x = -114 Reorder the terms: 2x + 72x2 = -114 Solving 2x + 72x2 = -114 Solving for variable 'x'. Reorder the terms: 114 + 2x + 72x2 = -114 + 114 Combine like terms: -114 + 114 = 0 114 + 2x + 72x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + x + 36x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(57 + x + 36x2)' equal to zero and attempt to solve: Simplifying 57 + x + 36x2 = 0 Solving 57 + x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 1.583333333 + 0.02777777778x + x2 = 0 Move the constant term to the right: Add '-1.583333333' to each side of the equation. 1.583333333 + 0.02777777778x + -1.583333333 + x2 = 0 + -1.583333333 Reorder the terms: 1.583333333 + -1.583333333 + 0.02777777778x + x2 = 0 + -1.583333333 Combine like terms: 1.583333333 + -1.583333333 = 0.000000000 0.000000000 + 0.02777777778x + x2 = 0 + -1.583333333 0.02777777778x + x2 = 0 + -1.583333333 Combine like terms: 0 + -1.583333333 = -1.583333333 0.02777777778x + x2 = -1.583333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02777777778x + 0.25 + x2 = -1.583333333 + 0.25 Reorder the terms: 0.25 + 0.02777777778x + x2 = -1.583333333 + 0.25 Combine like terms: -1.583333333 + 0.25 = -1.333333333 0.25 + 0.02777777778x + x2 = -1.333333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.333333333 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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