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Simplifying -16t2 + 70t + 4 = 30 Reorder the terms: 4 + 70t + -16t2 = 30 Solving 4 + 70t + -16t2 = 30 Solving for variable 't'. Reorder the terms: 4 + -30 + 70t + -16t2 = 30 + -30 Combine like terms: 4 + -30 = -26 -26 + 70t + -16t2 = 30 + -30 Combine like terms: 30 + -30 = 0 -26 + 70t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 35t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 35t + -8t2)' equal to zero and attempt to solve: Simplifying -13 + 35t + -8t2 = 0 Solving -13 + 35t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.625 + -4.375t + t2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -4.375t + -1.625 + t2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -4.375t + t2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -4.375t + t2 = 0 + -1.625 -4.375t + t2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -4.375t + t2 = -1.625 The t term is -4.375t. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375t + 4.78515625 + t2 = -1.625 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = -1.625 + 4.78515625 Combine like terms: -1.625 + 4.78515625 = 3.16015625 4.78515625 + -4.375t + t2 = 3.16015625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 3.16015625 Calculate the square root of the right side: 1.777682832 Break this problem into two subproblems by setting (t + -2.1875) equal to 1.777682832 and -1.777682832.Subproblem 1
t + -2.1875 = 1.777682832 Simplifying t + -2.1875 = 1.777682832 Reorder the terms: -2.1875 + t = 1.777682832 Solving -2.1875 + t = 1.777682832 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = 1.777682832 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 1.777682832 + 2.1875 t = 1.777682832 + 2.1875 Combine like terms: 1.777682832 + 2.1875 = 3.965182832 t = 3.965182832 Simplifying t = 3.965182832Subproblem 2
t + -2.1875 = -1.777682832 Simplifying t + -2.1875 = -1.777682832 Reorder the terms: -2.1875 + t = -1.777682832 Solving -2.1875 + t = -1.777682832 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = -1.777682832 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -1.777682832 + 2.1875 t = -1.777682832 + 2.1875 Combine like terms: -1.777682832 + 2.1875 = 0.409817168 t = 0.409817168 Simplifying t = 0.409817168Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.965182832, 0.409817168}Solution
t = {3.965182832, 0.409817168}
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