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Simplifying -16t2 + 148t + 30 = 0 Reorder the terms: 30 + 148t + -16t2 = 0 Solving 30 + 148t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 74t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 74t + -8t2)' equal to zero and attempt to solve: Simplifying 15 + 74t + -8t2 = 0 Solving 15 + 74t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -9.25t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -9.25t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -9.25t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -9.25t + t2 = 0 + 1.875 -9.25t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -9.25t + t2 = 1.875 The t term is -9.25t. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25t + 21.390625 + t2 = 1.875 + 21.390625 Reorder the terms: 21.390625 + -9.25t + t2 = 1.875 + 21.390625 Combine like terms: 1.875 + 21.390625 = 23.265625 21.390625 + -9.25t + t2 = 23.265625 Factor a perfect square on the left side: (t + -4.625)(t + -4.625) = 23.265625 Calculate the square root of the right side: 4.823445345 Break this problem into two subproblems by setting (t + -4.625) equal to 4.823445345 and -4.823445345.Subproblem 1
t + -4.625 = 4.823445345 Simplifying t + -4.625 = 4.823445345 Reorder the terms: -4.625 + t = 4.823445345 Solving -4.625 + t = 4.823445345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = 4.823445345 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = 4.823445345 + 4.625 t = 4.823445345 + 4.625 Combine like terms: 4.823445345 + 4.625 = 9.448445345 t = 9.448445345 Simplifying t = 9.448445345Subproblem 2
t + -4.625 = -4.823445345 Simplifying t + -4.625 = -4.823445345 Reorder the terms: -4.625 + t = -4.823445345 Solving -4.625 + t = -4.823445345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + t = -4.823445345 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + t = -4.823445345 + 4.625 t = -4.823445345 + 4.625 Combine like terms: -4.823445345 + 4.625 = -0.198445345 t = -0.198445345 Simplifying t = -0.198445345Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.448445345, -0.198445345}Solution
t = {9.448445345, -0.198445345}
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