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Simplifying 0 = -16t2 + 128t + 380 Reorder the terms: 0 = 380 + 128t + -16t2 Solving 0 = 380 + 128t + -16t2 Solving for variable 't'. Combine like terms: 0 + -380 = -380 -380 + -128t + 16t2 = 380 + 128t + -16t2 + -380 + -128t + 16t2 Reorder the terms: -380 + -128t + 16t2 = 380 + -380 + 128t + -128t + -16t2 + 16t2 Combine like terms: 380 + -380 = 0 -380 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2 -380 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 -380 + -128t + 16t2 = 0 + -16t2 + 16t2 -380 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -380 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-95 + -32t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-95 + -32t + 4t2)' equal to zero and attempt to solve: Simplifying -95 + -32t + 4t2 = 0 Solving -95 + -32t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -23.75 + -8t + t2 = 0 Move the constant term to the right: Add '23.75' to each side of the equation. -23.75 + -8t + 23.75 + t2 = 0 + 23.75 Reorder the terms: -23.75 + 23.75 + -8t + t2 = 0 + 23.75 Combine like terms: -23.75 + 23.75 = 0.00 0.00 + -8t + t2 = 0 + 23.75 -8t + t2 = 0 + 23.75 Combine like terms: 0 + 23.75 = 23.75 -8t + t2 = 23.75 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 23.75 + 16 Reorder the terms: 16 + -8t + t2 = 23.75 + 16 Combine like terms: 23.75 + 16 = 39.75 16 + -8t + t2 = 39.75 Factor a perfect square on the left side: (t + -4)(t + -4) = 39.75 Calculate the square root of the right side: 6.304760106 Break this problem into two subproblems by setting (t + -4) equal to 6.304760106 and -6.304760106.Subproblem 1
t + -4 = 6.304760106 Simplifying t + -4 = 6.304760106 Reorder the terms: -4 + t = 6.304760106 Solving -4 + t = 6.304760106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 6.304760106 + 4 Combine like terms: -4 + 4 = 0 0 + t = 6.304760106 + 4 t = 6.304760106 + 4 Combine like terms: 6.304760106 + 4 = 10.304760106 t = 10.304760106 Simplifying t = 10.304760106Subproblem 2
t + -4 = -6.304760106 Simplifying t + -4 = -6.304760106 Reorder the terms: -4 + t = -6.304760106 Solving -4 + t = -6.304760106 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -6.304760106 + 4 Combine like terms: -4 + 4 = 0 0 + t = -6.304760106 + 4 t = -6.304760106 + 4 Combine like terms: -6.304760106 + 4 = -2.304760106 t = -2.304760106 Simplifying t = -2.304760106Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.304760106, -2.304760106}Solution
t = {10.304760106, -2.304760106}
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