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Simplifying -16t2 + 112t + 124 = 0 Reorder the terms: 124 + 112t + -16t2 = 0 Solving 124 + 112t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(31 + 28t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(31 + 28t + -4t2)' equal to zero and attempt to solve: Simplifying 31 + 28t + -4t2 = 0 Solving 31 + 28t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.75 + -7t + t2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + -7t + 7.75 + t2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + -7t + t2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + -7t + t2 = 0 + 7.75 -7t + t2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 -7t + t2 = 7.75 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 7.75 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 7.75 + 12.25 Combine like terms: 7.75 + 12.25 = 20 12.25 + -7t + t2 = 20 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -3.5) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -3.5 = 4.472135955 Simplifying t + -3.5 = 4.472135955 Reorder the terms: -3.5 + t = 4.472135955 Solving -3.5 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 4.472135955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 4.472135955 + 3.5 t = 4.472135955 + 3.5 Combine like terms: 4.472135955 + 3.5 = 7.972135955 t = 7.972135955 Simplifying t = 7.972135955Subproblem 2
t + -3.5 = -4.472135955 Simplifying t + -3.5 = -4.472135955 Reorder the terms: -3.5 + t = -4.472135955 Solving -3.5 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -4.472135955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -4.472135955 + 3.5 t = -4.472135955 + 3.5 Combine like terms: -4.472135955 + 3.5 = -0.972135955 t = -0.972135955 Simplifying t = -0.972135955Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.972135955, -0.972135955}Solution
t = {7.972135955, -0.972135955}
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