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Simplifying 0 = 13x2 + -32x + 28 Reorder the terms: 0 = 28 + -32x + 13x2 Solving 0 = 28 + -32x + 13x2 Solving for variable 'x'. Combine like terms: 0 + -28 = -28 -28 + 32x + -13x2 = 28 + -32x + 13x2 + -28 + 32x + -13x2 Reorder the terms: -28 + 32x + -13x2 = 28 + -28 + -32x + 32x + 13x2 + -13x2 Combine like terms: 28 + -28 = 0 -28 + 32x + -13x2 = 0 + -32x + 32x + 13x2 + -13x2 -28 + 32x + -13x2 = -32x + 32x + 13x2 + -13x2 Combine like terms: -32x + 32x = 0 -28 + 32x + -13x2 = 0 + 13x2 + -13x2 -28 + 32x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -28 + 32x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 2.153846154 + -2.461538462x + x2 = 0 Move the constant term to the right: Add '-2.153846154' to each side of the equation. 2.153846154 + -2.461538462x + -2.153846154 + x2 = 0 + -2.153846154 Reorder the terms: 2.153846154 + -2.153846154 + -2.461538462x + x2 = 0 + -2.153846154 Combine like terms: 2.153846154 + -2.153846154 = 0.000000000 0.000000000 + -2.461538462x + x2 = 0 + -2.153846154 -2.461538462x + x2 = 0 + -2.153846154 Combine like terms: 0 + -2.153846154 = -2.153846154 -2.461538462x + x2 = -2.153846154 The x term is -2.461538462x. Take half its coefficient (-1.230769231). Square it (1.514792900) and add it to both sides. Add '1.514792900' to each side of the equation. -2.461538462x + 1.514792900 + x2 = -2.153846154 + 1.514792900 Reorder the terms: 1.514792900 + -2.461538462x + x2 = -2.153846154 + 1.514792900 Combine like terms: -2.153846154 + 1.514792900 = -0.639053254 1.514792900 + -2.461538462x + x2 = -0.639053254 Factor a perfect square on the left side: (x + -1.230769231)(x + -1.230769231) = -0.639053254 Can't calculate square root of the right side. The solution to this equation could not be determined.
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