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Simplifying 0 = 16t2 + 100t + -96 Reorder the terms: 0 = -96 + 100t + 16t2 Solving 0 = -96 + 100t + 16t2 Solving for variable 't'. Combine like terms: 0 + 96 = 96 96 + -100t + -16t2 = -96 + 100t + 16t2 + 96 + -100t + -16t2 Reorder the terms: 96 + -100t + -16t2 = -96 + 96 + 100t + -100t + 16t2 + -16t2 Combine like terms: -96 + 96 = 0 96 + -100t + -16t2 = 0 + 100t + -100t + 16t2 + -16t2 96 + -100t + -16t2 = 100t + -100t + 16t2 + -16t2 Combine like terms: 100t + -100t = 0 96 + -100t + -16t2 = 0 + 16t2 + -16t2 96 + -100t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 96 + -100t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -25t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -25t + -4t2)' equal to zero and attempt to solve: Simplifying 24 + -25t + -4t2 = 0 Solving 24 + -25t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6 + 6.25t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 6.25t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 6.25t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6.25t + t2 = 0 + 6 6.25t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 6.25t + t2 = 6 The t term is 6.25t. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25t + 9.765625 + t2 = 6 + 9.765625 Reorder the terms: 9.765625 + 6.25t + t2 = 6 + 9.765625 Combine like terms: 6 + 9.765625 = 15.765625 9.765625 + 6.25t + t2 = 15.765625 Factor a perfect square on the left side: (t + 3.125)(t + 3.125) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (t + 3.125) equal to 3.970595044 and -3.970595044.Subproblem 1
t + 3.125 = 3.970595044 Simplifying t + 3.125 = 3.970595044 Reorder the terms: 3.125 + t = 3.970595044 Solving 3.125 + t = 3.970595044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = 3.970595044 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = 3.970595044 + -3.125 t = 3.970595044 + -3.125 Combine like terms: 3.970595044 + -3.125 = 0.845595044 t = 0.845595044 Simplifying t = 0.845595044Subproblem 2
t + 3.125 = -3.970595044 Simplifying t + 3.125 = -3.970595044 Reorder the terms: 3.125 + t = -3.970595044 Solving 3.125 + t = -3.970595044 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + t = -3.970595044 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + t = -3.970595044 + -3.125 t = -3.970595044 + -3.125 Combine like terms: -3.970595044 + -3.125 = -7.095595044 t = -7.095595044 Simplifying t = -7.095595044Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.845595044, -7.095595044}Solution
t = {0.845595044, -7.095595044}
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