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Simplifying 15x2 + 1193.4 + -270x = -18x + x2 + 1 Reorder the terms: 1193.4 + -270x + 15x2 = -18x + x2 + 1 Reorder the terms: 1193.4 + -270x + 15x2 = 1 + -18x + x2 Solving 1193.4 + -270x + 15x2 = 1 + -18x + x2 Solving for variable 'x'. Reorder the terms: 1193.4 + -1 + -270x + 18x + 15x2 + -1x2 = 1 + -18x + x2 + -1 + 18x + -1x2 Combine like terms: 1193.4 + -1 = 1192.4 1192.4 + -270x + 18x + 15x2 + -1x2 = 1 + -18x + x2 + -1 + 18x + -1x2 Combine like terms: -270x + 18x = -252x 1192.4 + -252x + 15x2 + -1x2 = 1 + -18x + x2 + -1 + 18x + -1x2 Combine like terms: 15x2 + -1x2 = 14x2 1192.4 + -252x + 14x2 = 1 + -18x + x2 + -1 + 18x + -1x2 Reorder the terms: 1192.4 + -252x + 14x2 = 1 + -1 + -18x + 18x + x2 + -1x2 Combine like terms: 1 + -1 = 0 1192.4 + -252x + 14x2 = 0 + -18x + 18x + x2 + -1x2 1192.4 + -252x + 14x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 1192.4 + -252x + 14x2 = 0 + x2 + -1x2 1192.4 + -252x + 14x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1192.4 + -252x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 85.17142857 + -18x + x2 = 0 Move the constant term to the right: Add '-85.17142857' to each side of the equation. 85.17142857 + -18x + -85.17142857 + x2 = 0 + -85.17142857 Reorder the terms: 85.17142857 + -85.17142857 + -18x + x2 = 0 + -85.17142857 Combine like terms: 85.17142857 + -85.17142857 = 0.00000000 0.00000000 + -18x + x2 = 0 + -85.17142857 -18x + x2 = 0 + -85.17142857 Combine like terms: 0 + -85.17142857 = -85.17142857 -18x + x2 = -85.17142857 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -85.17142857 + 81 Reorder the terms: 81 + -18x + x2 = -85.17142857 + 81 Combine like terms: -85.17142857 + 81 = -4.17142857 81 + -18x + x2 = -4.17142857 Factor a perfect square on the left side: (x + -9)(x + -9) = -4.17142857 Can't calculate square root of the right side. The solution to this equation could not be determined.
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