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Simplifying -16t2 + 30t + 1000 = 0 Reorder the terms: 1000 + 30t + -16t2 = 0 Solving 1000 + 30t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(500 + 15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(500 + 15t + -8t2)' equal to zero and attempt to solve: Simplifying 500 + 15t + -8t2 = 0 Solving 500 + 15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -62.5 + -1.875t + t2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -1.875t + 62.5 + t2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -1.875t + t2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -1.875t + t2 = 0 + 62.5 -1.875t + t2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -1.875t + t2 = 62.5 The t term is -1.875t. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875t + 0.87890625 + t2 = 62.5 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 62.5 + 0.87890625 Combine like terms: 62.5 + 0.87890625 = 63.37890625 0.87890625 + -1.875t + t2 = 63.37890625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 63.37890625 Calculate the square root of the right side: 7.961087002 Break this problem into two subproblems by setting (t + -0.9375) equal to 7.961087002 and -7.961087002.Subproblem 1
t + -0.9375 = 7.961087002 Simplifying t + -0.9375 = 7.961087002 Reorder the terms: -0.9375 + t = 7.961087002 Solving -0.9375 + t = 7.961087002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = 7.961087002 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 7.961087002 + 0.9375 t = 7.961087002 + 0.9375 Combine like terms: 7.961087002 + 0.9375 = 8.898587002 t = 8.898587002 Simplifying t = 8.898587002Subproblem 2
t + -0.9375 = -7.961087002 Simplifying t + -0.9375 = -7.961087002 Reorder the terms: -0.9375 + t = -7.961087002 Solving -0.9375 + t = -7.961087002 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = -7.961087002 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -7.961087002 + 0.9375 t = -7.961087002 + 0.9375 Combine like terms: -7.961087002 + 0.9375 = -7.023587002 t = -7.023587002 Simplifying t = -7.023587002Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.898587002, -7.023587002}Solution
t = {8.898587002, -7.023587002}
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