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Simplifying (7t + -2)(3t + 1) = -3(1 + -3t) Reorder the terms: (-2 + 7t)(3t + 1) = -3(1 + -3t) Reorder the terms: (-2 + 7t)(1 + 3t) = -3(1 + -3t) Multiply (-2 + 7t) * (1 + 3t) (-2(1 + 3t) + 7t * (1 + 3t)) = -3(1 + -3t) ((1 * -2 + 3t * -2) + 7t * (1 + 3t)) = -3(1 + -3t) ((-2 + -6t) + 7t * (1 + 3t)) = -3(1 + -3t) (-2 + -6t + (1 * 7t + 3t * 7t)) = -3(1 + -3t) (-2 + -6t + (7t + 21t2)) = -3(1 + -3t) Combine like terms: -6t + 7t = 1t (-2 + 1t + 21t2) = -3(1 + -3t) -2 + 1t + 21t2 = (1 * -3 + -3t * -3) -2 + 1t + 21t2 = (-3 + 9t) Solving -2 + 1t + 21t2 = -3 + 9t Solving for variable 't'. Reorder the terms: -2 + 3 + 1t + -9t + 21t2 = -3 + 9t + 3 + -9t Combine like terms: -2 + 3 = 1 1 + 1t + -9t + 21t2 = -3 + 9t + 3 + -9t Combine like terms: 1t + -9t = -8t 1 + -8t + 21t2 = -3 + 9t + 3 + -9t Reorder the terms: 1 + -8t + 21t2 = -3 + 3 + 9t + -9t Combine like terms: -3 + 3 = 0 1 + -8t + 21t2 = 0 + 9t + -9t 1 + -8t + 21t2 = 9t + -9t Combine like terms: 9t + -9t = 0 1 + -8t + 21t2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.04761904762 + -0.380952381t + t2 = 0 Move the constant term to the right: Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.380952381t + -0.04761904762 + t2 = 0 + -0.04761904762 Reorder the terms: 0.04761904762 + -0.04761904762 + -0.380952381t + t2 = 0 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + -0.380952381t + t2 = 0 + -0.04761904762 -0.380952381t + t2 = 0 + -0.04761904762 Combine like terms: 0 + -0.04761904762 = -0.04761904762 -0.380952381t + t2 = -0.04761904762 The t term is -0.380952381t. Take half its coefficient (-0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. -0.380952381t + 0.03628117915 + t2 = -0.04761904762 + 0.03628117915 Reorder the terms: 0.03628117915 + -0.380952381t + t2 = -0.04761904762 + 0.03628117915 Combine like terms: -0.04761904762 + 0.03628117915 = -0.01133786847 0.03628117915 + -0.380952381t + t2 = -0.01133786847 Factor a perfect square on the left side: (t + -0.1904761905)(t + -0.1904761905) = -0.01133786847 Can't calculate square root of the right side. The solution to this equation could not be determined.
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