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Simplifying 13x2 + 12x + 15 = x + 10 Reorder the terms: 15 + 12x + 13x2 = x + 10 Reorder the terms: 15 + 12x + 13x2 = 10 + x Solving 15 + 12x + 13x2 = 10 + x Solving for variable 'x'. Reorder the terms: 15 + -10 + 12x + -1x + 13x2 = 10 + x + -10 + -1x Combine like terms: 15 + -10 = 5 5 + 12x + -1x + 13x2 = 10 + x + -10 + -1x Combine like terms: 12x + -1x = 11x 5 + 11x + 13x2 = 10 + x + -10 + -1x Reorder the terms: 5 + 11x + 13x2 = 10 + -10 + x + -1x Combine like terms: 10 + -10 = 0 5 + 11x + 13x2 = 0 + x + -1x 5 + 11x + 13x2 = x + -1x Combine like terms: x + -1x = 0 5 + 11x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3846153846 + 0.8461538462x + x2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + 0.8461538462x + -0.3846153846 + x2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + 0.8461538462x + x2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + 0.8461538462x + x2 = 0 + -0.3846153846 0.8461538462x + x2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 0.8461538462x + x2 = -0.3846153846 The x term is 0.8461538462x. Take half its coefficient (0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. 0.8461538462x + 0.1789940829 + x2 = -0.3846153846 + 0.1789940829 Reorder the terms: 0.1789940829 + 0.8461538462x + x2 = -0.3846153846 + 0.1789940829 Combine like terms: -0.3846153846 + 0.1789940829 = -0.2056213017 0.1789940829 + 0.8461538462x + x2 = -0.2056213017 Factor a perfect square on the left side: (x + 0.4230769231)(x + 0.4230769231) = -0.2056213017 Can't calculate square root of the right side. The solution to this equation could not be determined.
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