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Simplifying -16t2 + 120t + 56 = 0 Reorder the terms: 56 + 120t + -16t2 = 0 Solving 56 + 120t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(7 + 15t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + 15t + -2t2)' equal to zero and attempt to solve: Simplifying 7 + 15t + -2t2 = 0 Solving 7 + 15t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.5 + -7.5t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -7.5t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -7.5t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -7.5t + t2 = 0 + 3.5 -7.5t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -7.5t + t2 = 3.5 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = 3.5 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 3.5 + 14.0625 Combine like terms: 3.5 + 14.0625 = 17.5625 14.0625 + -7.5t + t2 = 17.5625 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (t + -3.75) equal to 4.190763654 and -4.190763654.Subproblem 1
t + -3.75 = 4.190763654 Simplifying t + -3.75 = 4.190763654 Reorder the terms: -3.75 + t = 4.190763654 Solving -3.75 + t = 4.190763654 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 4.190763654 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 4.190763654 + 3.75 t = 4.190763654 + 3.75 Combine like terms: 4.190763654 + 3.75 = 7.940763654 t = 7.940763654 Simplifying t = 7.940763654Subproblem 2
t + -3.75 = -4.190763654 Simplifying t + -3.75 = -4.190763654 Reorder the terms: -3.75 + t = -4.190763654 Solving -3.75 + t = -4.190763654 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -4.190763654 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -4.190763654 + 3.75 t = -4.190763654 + 3.75 Combine like terms: -4.190763654 + 3.75 = -0.440763654 t = -0.440763654 Simplifying t = -0.440763654Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.940763654, -0.440763654}Solution
t = {7.940763654, -0.440763654}
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