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Simplifying 70 = 10t + 16t2 Solving 70 = 10t + 16t2 Solving for variable 't'. Reorder the terms: 70 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2 Combine like terms: 10t + -10t = 0 70 + -10t + -16t2 = 0 + 16t2 + -16t2 70 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 70 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -5t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -5t + -8t2)' equal to zero and attempt to solve: Simplifying 35 + -5t + -8t2 = 0 Solving 35 + -5t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + 0.625t + t2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 0.625t + 4.375 + t2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 0.625t + t2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 0.625t + t2 = 0 + 4.375 0.625t + t2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 0.625t + t2 = 4.375 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 4.375 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 4.375 + 0.09765625 Combine like terms: 4.375 + 0.09765625 = 4.47265625 0.09765625 + 0.625t + t2 = 4.47265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 4.47265625 Calculate the square root of the right side: 2.114865539 Break this problem into two subproblems by setting (t + 0.3125) equal to 2.114865539 and -2.114865539.Subproblem 1
t + 0.3125 = 2.114865539 Simplifying t + 0.3125 = 2.114865539 Reorder the terms: 0.3125 + t = 2.114865539 Solving 0.3125 + t = 2.114865539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 2.114865539 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 2.114865539 + -0.3125 t = 2.114865539 + -0.3125 Combine like terms: 2.114865539 + -0.3125 = 1.802365539 t = 1.802365539 Simplifying t = 1.802365539Subproblem 2
t + 0.3125 = -2.114865539 Simplifying t + 0.3125 = -2.114865539 Reorder the terms: 0.3125 + t = -2.114865539 Solving 0.3125 + t = -2.114865539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -2.114865539 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -2.114865539 + -0.3125 t = -2.114865539 + -0.3125 Combine like terms: -2.114865539 + -0.3125 = -2.427365539 t = -2.427365539 Simplifying t = -2.427365539Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.802365539, -2.427365539}Solution
t = {1.802365539, -2.427365539}
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