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Simplifying 4t2 + -25t + 28 = 0 Reorder the terms: 28 + -25t + 4t2 = 0 Solving 28 + -25t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + -6.25t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6.25t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -6.25t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6.25t + t2 = 0 + -7 -6.25t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6.25t + t2 = -7 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = -7 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = -7 + 9.765625 Combine like terms: -7 + 9.765625 = 2.765625 9.765625 + -6.25t + t2 = 2.765625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (t + -3.125) equal to 1.663016837 and -1.663016837.Subproblem 1
t + -3.125 = 1.663016837 Simplifying t + -3.125 = 1.663016837 Reorder the terms: -3.125 + t = 1.663016837 Solving -3.125 + t = 1.663016837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 1.663016837 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 1.663016837 + 3.125 t = 1.663016837 + 3.125 Combine like terms: 1.663016837 + 3.125 = 4.788016837 t = 4.788016837 Simplifying t = 4.788016837Subproblem 2
t + -3.125 = -1.663016837 Simplifying t + -3.125 = -1.663016837 Reorder the terms: -3.125 + t = -1.663016837 Solving -3.125 + t = -1.663016837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -1.663016837 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -1.663016837 + 3.125 t = -1.663016837 + 3.125 Combine like terms: -1.663016837 + 3.125 = 1.461983163 t = 1.461983163 Simplifying t = 1.461983163Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.788016837, 1.461983163}
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