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Simplifying -15t2 + 90t + 10 = 0 Reorder the terms: 10 + 90t + -15t2 = 0 Solving 10 + 90t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 18t + -3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + 18t + -3t2)' equal to zero and attempt to solve: Simplifying 2 + 18t + -3t2 = 0 Solving 2 + 18t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + -6t + t2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -6t + 0.6666666667 + t2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -6t + t2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -6t + t2 = 0 + 0.6666666667 -6t + t2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -6t + t2 = 0.6666666667 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 = 0.6666666667 + 9 Reorder the terms: 9 + -6t + t2 = 0.6666666667 + 9 Combine like terms: 0.6666666667 + 9 = 9.6666666667 9 + -6t + t2 = 9.6666666667 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.6666666667 Calculate the square root of the right side: 3.109126351 Break this problem into two subproblems by setting (t + -3) equal to 3.109126351 and -3.109126351.Subproblem 1
t + -3 = 3.109126351 Simplifying t + -3 = 3.109126351 Reorder the terms: -3 + t = 3.109126351 Solving -3 + t = 3.109126351 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 = 3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.109126351 + 3 t = 3.109126351 + 3 Combine like terms: 3.109126351 + 3 = 6.109126351 t = 6.109126351 Simplifying t = 6.109126351Subproblem 2
t + -3 = -3.109126351 Simplifying t + -3 = -3.109126351 Reorder the terms: -3 + t = -3.109126351 Solving -3 + t = -3.109126351 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 = -3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.109126351 + 3 t = -3.109126351 + 3 Combine like terms: -3.109126351 + 3 = -0.109126351 t = -0.109126351 Simplifying t = -0.109126351Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.109126351, -0.109126351}Solution
t = {6.109126351, -0.109126351}
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