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Simplifying -3t2 + 30t + -21 = 0 Reorder the terms: -21 + 30t + -3t2 = 0 Solving -21 + 30t + -3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 10t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying -7 + 10t + -1t2 = 0 Solving -7 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -10t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -10t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -10t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10t + t2 = 0 + -7 -10t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -10t + t2 = -7 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 = -7 + 25 Reorder the terms: 25 + -10t + t2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + -10t + t2 = 18 Factor a perfect square on the left side: (t + -5)(t + -5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + -5) equal to 4.242640687 and -4.242640687.Subproblem 1
t + -5 = 4.242640687 Simplifying t + -5 = 4.242640687 Reorder the terms: -5 + t = 4.242640687 Solving -5 + t = 4.242640687 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 = 4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + t = 4.242640687 + 5 t = 4.242640687 + 5 Combine like terms: 4.242640687 + 5 = 9.242640687 t = 9.242640687 Simplifying t = 9.242640687Subproblem 2
t + -5 = -4.242640687 Simplifying t + -5 = -4.242640687 Reorder the terms: -5 + t = -4.242640687 Solving -5 + t = -4.242640687 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 = -4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + t = -4.242640687 + 5 t = -4.242640687 + 5 Combine like terms: -4.242640687 + 5 = 0.757359313 t = 0.757359313 Simplifying t = 0.757359313Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.242640687, 0.757359313}Solution
t = {9.242640687, 0.757359313}
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