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Simplifying -16t2 + 30t + 2 = 0 Reorder the terms: 2 + 30t + -16t2 = 0 Solving 2 + 30t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 15t + -8t2)' equal to zero and attempt to solve: Simplifying 1 + 15t + -8t2 = 0 Solving 1 + 15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -1.875t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.875t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.875t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.875t + t2 = 0 + 0.125 -1.875t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.875t + t2 = 0.125 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 = 0.125 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 0.125 + 0.87890625 Combine like terms: 0.125 + 0.87890625 = 1.00390625 0.87890625 + -1.875t + t2 = 1.00390625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 1.00390625 Calculate the square root of the right side: 1.001951221 Break this problem into two subproblems by setting (t + -0.9375) equal to 1.001951221 and -1.001951221.Subproblem 1
t + -0.9375 = 1.001951221 Simplifying t + -0.9375 = 1.001951221 Reorder the terms: -0.9375 + t = 1.001951221 Solving -0.9375 + t = 1.001951221 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 = 1.001951221 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 1.001951221 + 0.9375 t = 1.001951221 + 0.9375 Combine like terms: 1.001951221 + 0.9375 = 1.939451221 t = 1.939451221 Simplifying t = 1.939451221Subproblem 2
t + -0.9375 = -1.001951221 Simplifying t + -0.9375 = -1.001951221 Reorder the terms: -0.9375 + t = -1.001951221 Solving -0.9375 + t = -1.001951221 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 = -1.001951221 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -1.001951221 + 0.9375 t = -1.001951221 + 0.9375 Combine like terms: -1.001951221 + 0.9375 = -0.064451221 t = -0.064451221 Simplifying t = -0.064451221Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.939451221, -0.064451221}Solution
t = {1.939451221, -0.064451221}
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