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Simplifying 30 = -16t2 + 100t + 50 Reorder the terms: 30 = 50 + 100t + -16t2 Solving 30 = 50 + 100t + -16t2 Solving for variable 't'. Combine like terms: 30 + -50 = -20 -20 + -100t + 16t2 = 50 + 100t + -16t2 + -50 + -100t + 16t2 Reorder the terms: -20 + -100t + 16t2 = 50 + -50 + 100t + -100t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -20 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 -20 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 -20 + -100t + 16t2 = 0 + -16t2 + 16t2 -20 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -25t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -25t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + -25t + 4t2 = 0 Solving -5 + -25t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -6.25t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -6.25t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -6.25t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -6.25t + t2 = 0 + 1.25 -6.25t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -6.25t + t2 = 1.25 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 = 1.25 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = 1.25 + 9.765625 Combine like terms: 1.25 + 9.765625 = 11.015625 9.765625 + -6.25t + t2 = 11.015625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 11.015625 Calculate the square root of the right side: 3.318979512 Break this problem into two subproblems by setting (t + -3.125) equal to 3.318979512 and -3.318979512.Subproblem 1
t + -3.125 = 3.318979512 Simplifying t + -3.125 = 3.318979512 Reorder the terms: -3.125 + t = 3.318979512 Solving -3.125 + t = 3.318979512 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 = 3.318979512 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 3.318979512 + 3.125 t = 3.318979512 + 3.125 Combine like terms: 3.318979512 + 3.125 = 6.443979512 t = 6.443979512 Simplifying t = 6.443979512Subproblem 2
t + -3.125 = -3.318979512 Simplifying t + -3.125 = -3.318979512 Reorder the terms: -3.125 + t = -3.318979512 Solving -3.125 + t = -3.318979512 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 = -3.318979512 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -3.318979512 + 3.125 t = -3.318979512 + 3.125 Combine like terms: -3.318979512 + 3.125 = -0.193979512 t = -0.193979512 Simplifying t = -0.193979512Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.443979512, -0.193979512}Solution
t = {6.443979512, -0.193979512}
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