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Simplifying 4t2 + 48t = -68 Reorder the terms: 48t + 4t2 = -68 Solving 48t + 4t2 = -68 Solving for variable 't'. Reorder the terms: 68 + 48t + 4t2 = -68 + 68 Combine like terms: -68 + 68 = 0 68 + 48t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(17 + 12t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(17 + 12t + t2)' equal to zero and attempt to solve: Simplifying 17 + 12t + t2 = 0 Solving 17 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 12t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + 12t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 12t + t2 = 0 + -17 12t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 12t + t2 = -17 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = -17 + 36 Reorder the terms: 36 + 12t + t2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + 12t + t2 = 19 Factor a perfect square on the left side: (t + 6)(t + 6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (t + 6) equal to 4.358898944 and -4.358898944.Subproblem 1
t + 6 = 4.358898944 Simplifying t + 6 = 4.358898944 Reorder the terms: 6 + t = 4.358898944 Solving 6 + t = 4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + t = 4.358898944 + -6 t = 4.358898944 + -6 Combine like terms: 4.358898944 + -6 = -1.641101056 t = -1.641101056 Simplifying t = -1.641101056Subproblem 2
t + 6 = -4.358898944 Simplifying t + 6 = -4.358898944 Reorder the terms: 6 + t = -4.358898944 Solving 6 + t = -4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + t = -4.358898944 + -6 t = -4.358898944 + -6 Combine like terms: -4.358898944 + -6 = -10.358898944 t = -10.358898944 Simplifying t = -10.358898944Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.641101056, -10.358898944}Solution
t = {-1.641101056, -10.358898944}
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