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Simplifying -16t2 + 36t + 4 = 0 Reorder the terms: 4 + 36t + -16t2 = 0 Solving 4 + 36t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 9t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 9t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 9t + -4t2 = 0 Solving 1 + 9t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -2.25t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.25t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.25t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.25t + t2 = 0 + 0.25 -2.25t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.25t + t2 = 0.25 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 0.25 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 0.25 + 1.265625 Combine like terms: 0.25 + 1.265625 = 1.515625 1.265625 + -2.25t + t2 = 1.515625 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (t + -1.125) equal to 1.231107225 and -1.231107225.Subproblem 1
t + -1.125 = 1.231107225 Simplifying t + -1.125 = 1.231107225 Reorder the terms: -1.125 + t = 1.231107225 Solving -1.125 + t = 1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.231107225 + 1.125 t = 1.231107225 + 1.125 Combine like terms: 1.231107225 + 1.125 = 2.356107225 t = 2.356107225 Simplifying t = 2.356107225Subproblem 2
t + -1.125 = -1.231107225 Simplifying t + -1.125 = -1.231107225 Reorder the terms: -1.125 + t = -1.231107225 Solving -1.125 + t = -1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.231107225 + 1.125 t = -1.231107225 + 1.125 Combine like terms: -1.231107225 + 1.125 = -0.106107225 t = -0.106107225 Simplifying t = -0.106107225Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.356107225, -0.106107225}Solution
t = {2.356107225, -0.106107225}
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