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Simplifying 7(t2 + 5t + -9) + t = t(7t + -2) * 13 Reorder the terms: 7(-9 + 5t + t2) + t = t(7t + -2) * 13 (-9 * 7 + 5t * 7 + t2 * 7) + t = t(7t + -2) * 13 (-63 + 35t + 7t2) + t = t(7t + -2) * 13 Reorder the terms: -63 + 35t + t + 7t2 = t(7t + -2) * 13 Combine like terms: 35t + t = 36t -63 + 36t + 7t2 = t(7t + -2) * 13 Reorder the terms: -63 + 36t + 7t2 = t(-2 + 7t) * 13 Reorder the terms for easier multiplication: -63 + 36t + 7t2 = 13t(-2 + 7t) -63 + 36t + 7t2 = (-2 * 13t + 7t * 13t) -63 + 36t + 7t2 = (-26t + 91t2) Solving -63 + 36t + 7t2 = -26t + 91t2 Solving for variable 't'. Reorder the terms: -63 + 36t + 26t + 7t2 + -91t2 = -26t + 91t2 + 26t + -91t2 Combine like terms: 36t + 26t = 62t -63 + 62t + 7t2 + -91t2 = -26t + 91t2 + 26t + -91t2 Combine like terms: 7t2 + -91t2 = -84t2 -63 + 62t + -84t2 = -26t + 91t2 + 26t + -91t2 Reorder the terms: -63 + 62t + -84t2 = -26t + 26t + 91t2 + -91t2 Combine like terms: -26t + 26t = 0 -63 + 62t + -84t2 = 0 + 91t2 + -91t2 -63 + 62t + -84t2 = 91t2 + -91t2 Combine like terms: 91t2 + -91t2 = 0 -63 + 62t + -84t2 = 0 Begin completing the square. Divide all terms by -84 the coefficient of the squared term: Divide each side by '-84'. 0.75 + -0.7380952381t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.7380952381t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.7380952381t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.7380952381t + t2 = 0 + -0.75 -0.7380952381t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.7380952381t + t2 = -0.75 The t term is -0.7380952381t. Take half its coefficient (-0.3690476191). Square it (0.1361961452) and add it to both sides. Add '0.1361961452' to each side of the equation. -0.7380952381t + 0.1361961452 + t2 = -0.75 + 0.1361961452 Reorder the terms: 0.1361961452 + -0.7380952381t + t2 = -0.75 + 0.1361961452 Combine like terms: -0.75 + 0.1361961452 = -0.6138038548 0.1361961452 + -0.7380952381t + t2 = -0.6138038548 Factor a perfect square on the left side: (t + -0.3690476191)(t + -0.3690476191) = -0.6138038548 Can't calculate square root of the right side. The solution to this equation could not be determined.
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