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Simplifying 6t3 + 6t2 + -70t = 0 Reorder the terms: -70t + 6t2 + 6t3 = 0 Solving -70t + 6t2 + 6t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(-35 + 3t + 3t2) = 0 Ignore the factor 2.Subproblem 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 '(-35 + 3t + 3t2)' equal to zero and attempt to solve: Simplifying -35 + 3t + 3t2 = 0 Solving -35 + 3t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + t + t2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + t + 11.66666667 + t2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + t + t2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + t + t2 = 0 + 11.66666667 t + t2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 t + t2 = 11.66666667 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 11.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 11.66666667 + 0.25 Combine like terms: 11.66666667 + 0.25 = 11.91666667 1.25 + t2 = 11.91666667 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 11.91666667 Calculate the square root of the right side: 3.45205253 Break this problem into two subproblems by setting (t + 0.5) equal to 3.45205253 and -3.45205253.Subproblem 1
t + 0.5 = 3.45205253 Simplifying t + 0.5 = 3.45205253 Reorder the terms: 0.5 + t = 3.45205253 Solving 0.5 + t = 3.45205253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 3.45205253 + -0.5 t = 3.45205253 + -0.5 Combine like terms: 3.45205253 + -0.5 = 2.95205253 t = 2.95205253 Simplifying t = 2.95205253Subproblem 2
t + 0.5 = -3.45205253 Simplifying t + 0.5 = -3.45205253 Reorder the terms: 0.5 + t = -3.45205253 Solving 0.5 + t = -3.45205253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -3.45205253 + -0.5 t = -3.45205253 + -0.5 Combine like terms: -3.45205253 + -0.5 = -3.95205253 t = -3.95205253 Simplifying t = -3.95205253Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.95205253, -3.95205253}Solution
t = {0, 2.95205253, -3.95205253}
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