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Simplifying 15t2 + 150t + 10 = 0 Reorder the terms: 10 + 150t + 15t2 = 0 Solving 10 + 150t + 15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 30t + 3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + 30t + 3t2)' equal to zero and attempt to solve: Simplifying 2 + 30t + 3t2 = 0 Solving 2 + 30t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 10t + t2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 10t + -0.6666666667 + t2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 10t + t2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 10t + t2 = 0 + -0.6666666667 10t + t2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 10t + t2 = -0.6666666667 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = -0.6666666667 + 25 Reorder the terms: 25 + 10t + t2 = -0.6666666667 + 25 Combine like terms: -0.6666666667 + 25 = 24.3333333333 25 + 10t + t2 = 24.3333333333 Factor a perfect square on the left side: (t + 5)(t + 5) = 24.3333333333 Calculate the square root of the right side: 4.932882862 Break this problem into two subproblems by setting (t + 5) equal to 4.932882862 and -4.932882862.Subproblem 1
t + 5 = 4.932882862 Simplifying t + 5 = 4.932882862 Reorder the terms: 5 + t = 4.932882862 Solving 5 + t = 4.932882862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 4.932882862 + -5 Combine like terms: 5 + -5 = 0 0 + t = 4.932882862 + -5 t = 4.932882862 + -5 Combine like terms: 4.932882862 + -5 = -0.067117138 t = -0.067117138 Simplifying t = -0.067117138Subproblem 2
t + 5 = -4.932882862 Simplifying t + 5 = -4.932882862 Reorder the terms: 5 + t = -4.932882862 Solving 5 + t = -4.932882862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -4.932882862 + -5 Combine like terms: 5 + -5 = 0 0 + t = -4.932882862 + -5 t = -4.932882862 + -5 Combine like terms: -4.932882862 + -5 = -9.932882862 t = -9.932882862 Simplifying t = -9.932882862Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.067117138, -9.932882862}Solution
t = {-0.067117138, -9.932882862}
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