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Simplifying -7t2 + 7t + 8t3 + -1t3 + 15t2 + -4t = 0 Reorder the terms: 7t + -4t + -7t2 + 15t2 + 8t3 + -1t3 = 0 Combine like terms: 7t + -4t = 3t 3t + -7t2 + 15t2 + 8t3 + -1t3 = 0 Combine like terms: -7t2 + 15t2 = 8t2 3t + 8t2 + 8t3 + -1t3 = 0 Combine like terms: 8t3 + -1t3 = 7t3 3t + 8t2 + 7t3 = 0 Solving 3t + 8t2 + 7t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(3 + 8t + 7t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(3 + 8t + 7t2)' equal to zero and attempt to solve: Simplifying 3 + 8t + 7t2 = 0 Solving 3 + 8t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 1.142857143t + t2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 1.142857143t + -0.4285714286 + t2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 1.142857143t + t2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 1.142857143t + t2 = 0 + -0.4285714286 1.142857143t + t2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 1.142857143t + t2 = -0.4285714286 The t term is 1.142857143t. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143t + 0.3265306123 + t2 = -0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143t + t2 = -0.4285714286 + 0.3265306123 Combine like terms: -0.4285714286 + 0.3265306123 = -0.1020408163 0.3265306123 + 1.142857143t + t2 = -0.1020408163 Factor a perfect square on the left side: (t + 0.5714285715)(t + 0.5714285715) = -0.1020408163 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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