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Simplifying -800 = -16t2 + 14t Reorder the terms: -800 = 14t + -16t2 Solving -800 = 14t + -16t2 Solving for variable 't'. Reorder the terms: -800 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2 Combine like terms: 14t + -14t = 0 -800 + -14t + 16t2 = 0 + -16t2 + 16t2 -800 + -14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -800 + -14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-400 + -7t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-400 + -7t + 8t2)' equal to zero and attempt to solve: Simplifying -400 + -7t + 8t2 = 0 Solving -400 + -7t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -50 + -0.875t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.875t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -0.875t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.875t + t2 = 0 + 50 -0.875t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.875t + t2 = 50 The t term is -0.875t. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875t + 0.19140625 + t2 = 50 + 0.19140625 Reorder the terms: 0.19140625 + -0.875t + t2 = 50 + 0.19140625 Combine like terms: 50 + 0.19140625 = 50.19140625 0.19140625 + -0.875t + t2 = 50.19140625 Factor a perfect square on the left side: (t + -0.4375)(t + -0.4375) = 50.19140625 Calculate the square root of the right side: 7.084589349 Break this problem into two subproblems by setting (t + -0.4375) equal to 7.084589349 and -7.084589349.Subproblem 1
t + -0.4375 = 7.084589349 Simplifying t + -0.4375 = 7.084589349 Reorder the terms: -0.4375 + t = 7.084589349 Solving -0.4375 + t = 7.084589349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = 7.084589349 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = 7.084589349 + 0.4375 t = 7.084589349 + 0.4375 Combine like terms: 7.084589349 + 0.4375 = 7.522089349 t = 7.522089349 Simplifying t = 7.522089349Subproblem 2
t + -0.4375 = -7.084589349 Simplifying t + -0.4375 = -7.084589349 Reorder the terms: -0.4375 + t = -7.084589349 Solving -0.4375 + t = -7.084589349 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = -7.084589349 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = -7.084589349 + 0.4375 t = -7.084589349 + 0.4375 Combine like terms: -7.084589349 + 0.4375 = -6.647089349 t = -6.647089349 Simplifying t = -6.647089349Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.522089349, -6.647089349}Solution
t = {7.522089349, -6.647089349}
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