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Simplifying 15t2 + 90t + -130 = 0 Reorder the terms: -130 + 90t + 15t2 = 0 Solving -130 + 90t + 15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-26 + 18t + 3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-26 + 18t + 3t2)' equal to zero and attempt to solve: Simplifying -26 + 18t + 3t2 = 0 Solving -26 + 18t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.666666667 + 6t + t2 = 0 Move the constant term to the right: Add '8.666666667' to each side of the equation. -8.666666667 + 6t + 8.666666667 + t2 = 0 + 8.666666667 Reorder the terms: -8.666666667 + 8.666666667 + 6t + t2 = 0 + 8.666666667 Combine like terms: -8.666666667 + 8.666666667 = 0.000000000 0.000000000 + 6t + t2 = 0 + 8.666666667 6t + t2 = 0 + 8.666666667 Combine like terms: 0 + 8.666666667 = 8.666666667 6t + t2 = 8.666666667 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 8.666666667 + 9 Reorder the terms: 9 + 6t + t2 = 8.666666667 + 9 Combine like terms: 8.666666667 + 9 = 17.666666667 9 + 6t + t2 = 17.666666667 Factor a perfect square on the left side: (t + 3)(t + 3) = 17.666666667 Calculate the square root of the right side: 4.203173404 Break this problem into two subproblems by setting (t + 3) equal to 4.203173404 and -4.203173404.Subproblem 1
t + 3 = 4.203173404 Simplifying t + 3 = 4.203173404 Reorder the terms: 3 + t = 4.203173404 Solving 3 + t = 4.203173404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 4.203173404 + -3 Combine like terms: 3 + -3 = 0 0 + t = 4.203173404 + -3 t = 4.203173404 + -3 Combine like terms: 4.203173404 + -3 = 1.203173404 t = 1.203173404 Simplifying t = 1.203173404Subproblem 2
t + 3 = -4.203173404 Simplifying t + 3 = -4.203173404 Reorder the terms: 3 + t = -4.203173404 Solving 3 + t = -4.203173404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -4.203173404 + -3 Combine like terms: 3 + -3 = 0 0 + t = -4.203173404 + -3 t = -4.203173404 + -3 Combine like terms: -4.203173404 + -3 = -7.203173404 t = -7.203173404 Simplifying t = -7.203173404Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.203173404, -7.203173404}Solution
t = {1.203173404, -7.203173404}
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