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Simplifying 9x2 + -97x + 312 = 6x2 + -58x + 158 Reorder the terms: 312 + -97x + 9x2 = 6x2 + -58x + 158 Reorder the terms: 312 + -97x + 9x2 = 158 + -58x + 6x2 Solving 312 + -97x + 9x2 = 158 + -58x + 6x2 Solving for variable 'x'. Reorder the terms: 312 + -158 + -97x + 58x + 9x2 + -6x2 = 158 + -58x + 6x2 + -158 + 58x + -6x2 Combine like terms: 312 + -158 = 154 154 + -97x + 58x + 9x2 + -6x2 = 158 + -58x + 6x2 + -158 + 58x + -6x2 Combine like terms: -97x + 58x = -39x 154 + -39x + 9x2 + -6x2 = 158 + -58x + 6x2 + -158 + 58x + -6x2 Combine like terms: 9x2 + -6x2 = 3x2 154 + -39x + 3x2 = 158 + -58x + 6x2 + -158 + 58x + -6x2 Reorder the terms: 154 + -39x + 3x2 = 158 + -158 + -58x + 58x + 6x2 + -6x2 Combine like terms: 158 + -158 = 0 154 + -39x + 3x2 = 0 + -58x + 58x + 6x2 + -6x2 154 + -39x + 3x2 = -58x + 58x + 6x2 + -6x2 Combine like terms: -58x + 58x = 0 154 + -39x + 3x2 = 0 + 6x2 + -6x2 154 + -39x + 3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 154 + -39x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 51.33333333 + -13x + x2 = 0 Move the constant term to the right: Add '-51.33333333' to each side of the equation. 51.33333333 + -13x + -51.33333333 + x2 = 0 + -51.33333333 Reorder the terms: 51.33333333 + -51.33333333 + -13x + x2 = 0 + -51.33333333 Combine like terms: 51.33333333 + -51.33333333 = 0.00000000 0.00000000 + -13x + x2 = 0 + -51.33333333 -13x + x2 = 0 + -51.33333333 Combine like terms: 0 + -51.33333333 = -51.33333333 -13x + x2 = -51.33333333 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -51.33333333 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -51.33333333 + 42.25 Combine like terms: -51.33333333 + 42.25 = -9.08333333 42.25 + -13x + x2 = -9.08333333 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = -9.08333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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