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Simplifying -16t2 + 224t + -10 = 0 Reorder the terms: -10 + 224t + -16t2 = 0 Solving -10 + 224t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 112t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 112t + -8t2)' equal to zero and attempt to solve: Simplifying -5 + 112t + -8t2 = 0 Solving -5 + 112t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.625 + -14t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -14t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -14t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -14t + t2 = 0 + -0.625 -14t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -14t + t2 = -0.625 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = -0.625 + 49 Reorder the terms: 49 + -14t + t2 = -0.625 + 49 Combine like terms: -0.625 + 49 = 48.375 49 + -14t + t2 = 48.375 Factor a perfect square on the left side: (t + -7)(t + -7) = 48.375 Calculate the square root of the right side: 6.955213872 Break this problem into two subproblems by setting (t + -7) equal to 6.955213872 and -6.955213872.Subproblem 1
t + -7 = 6.955213872 Simplifying t + -7 = 6.955213872 Reorder the terms: -7 + t = 6.955213872 Solving -7 + t = 6.955213872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 6.955213872 + 7 Combine like terms: -7 + 7 = 0 0 + t = 6.955213872 + 7 t = 6.955213872 + 7 Combine like terms: 6.955213872 + 7 = 13.955213872 t = 13.955213872 Simplifying t = 13.955213872Subproblem 2
t + -7 = -6.955213872 Simplifying t + -7 = -6.955213872 Reorder the terms: -7 + t = -6.955213872 Solving -7 + t = -6.955213872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -6.955213872 + 7 Combine like terms: -7 + 7 = 0 0 + t = -6.955213872 + 7 t = -6.955213872 + 7 Combine like terms: -6.955213872 + 7 = 0.044786128 t = 0.044786128 Simplifying t = 0.044786128Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.955213872, 0.044786128}Solution
t = {13.955213872, 0.044786128}
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