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Simplifying 30 = 16t2 + 64t Reorder the terms: 30 = 64t + 16t2 Solving 30 = 64t + 16t2 Solving for variable 't'. Reorder the terms: 30 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 30 + -64t + -16t2 = 0 + 16t2 + -16t2 30 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 30 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -32t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -32t + -8t2)' equal to zero and attempt to solve: Simplifying 15 + -32t + -8t2 = 0 Solving 15 + -32t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + 4t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 4t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 4t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 4t + t2 = 0 + 1.875 4t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 4t + t2 = 1.875 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 1.875 + 4 Reorder the terms: 4 + 4t + t2 = 1.875 + 4 Combine like terms: 1.875 + 4 = 5.875 4 + 4t + t2 = 5.875 Factor a perfect square on the left side: (t + 2)(t + 2) = 5.875 Calculate the square root of the right side: 2.423839929 Break this problem into two subproblems by setting (t + 2) equal to 2.423839929 and -2.423839929.Subproblem 1
t + 2 = 2.423839929 Simplifying t + 2 = 2.423839929 Reorder the terms: 2 + t = 2.423839929 Solving 2 + t = 2.423839929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 2.423839929 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.423839929 + -2 t = 2.423839929 + -2 Combine like terms: 2.423839929 + -2 = 0.423839929 t = 0.423839929 Simplifying t = 0.423839929Subproblem 2
t + 2 = -2.423839929 Simplifying t + 2 = -2.423839929 Reorder the terms: 2 + t = -2.423839929 Solving 2 + t = -2.423839929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -2.423839929 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.423839929 + -2 t = -2.423839929 + -2 Combine like terms: -2.423839929 + -2 = -4.423839929 t = -4.423839929 Simplifying t = -4.423839929Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.423839929, -4.423839929}Solution
t = {0.423839929, -4.423839929}
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