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Simplifying 28 = 16t2 + -46t Reorder the terms: 28 = -46t + 16t2 Solving 28 = -46t + 16t2 Solving for variable 't'. Reorder the terms: 28 + 46t + -16t2 = -46t + 46t + 16t2 + -16t2 Combine like terms: -46t + 46t = 0 28 + 46t + -16t2 = 0 + 16t2 + -16t2 28 + 46t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 28 + 46t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 23t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 23t + -8t2)' equal to zero and attempt to solve: Simplifying 14 + 23t + -8t2 = 0 Solving 14 + 23t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.75 + -2.875t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2.875t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2.875t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2.875t + t2 = 0 + 1.75 -2.875t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2.875t + t2 = 1.75 The t term is -2.875t. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875t + 2.06640625 + t2 = 1.75 + 2.06640625 Reorder the terms: 2.06640625 + -2.875t + t2 = 1.75 + 2.06640625 Combine like terms: 1.75 + 2.06640625 = 3.81640625 2.06640625 + -2.875t + t2 = 3.81640625 Factor a perfect square on the left side: (t + -1.4375)(t + -1.4375) = 3.81640625 Calculate the square root of the right side: 1.953562451 Break this problem into two subproblems by setting (t + -1.4375) equal to 1.953562451 and -1.953562451.Subproblem 1
t + -1.4375 = 1.953562451 Simplifying t + -1.4375 = 1.953562451 Reorder the terms: -1.4375 + t = 1.953562451 Solving -1.4375 + t = 1.953562451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = 1.953562451 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = 1.953562451 + 1.4375 t = 1.953562451 + 1.4375 Combine like terms: 1.953562451 + 1.4375 = 3.391062451 t = 3.391062451 Simplifying t = 3.391062451Subproblem 2
t + -1.4375 = -1.953562451 Simplifying t + -1.4375 = -1.953562451 Reorder the terms: -1.4375 + t = -1.953562451 Solving -1.4375 + t = -1.953562451 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = -1.953562451 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = -1.953562451 + 1.4375 t = -1.953562451 + 1.4375 Combine like terms: -1.953562451 + 1.4375 = -0.516062451 t = -0.516062451 Simplifying t = -0.516062451Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.391062451, -0.516062451}Solution
t = {3.391062451, -0.516062451}
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