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Simplifying -16t2 + 60t + 12 = 0 Reorder the terms: 12 + 60t + -16t2 = 0 Solving 12 + 60t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 15t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + 15t + -4t2)' equal to zero and attempt to solve: Simplifying 3 + 15t + -4t2 = 0 Solving 3 + 15t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -3.75t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -3.75t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -3.75t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -3.75t + t2 = 0 + 0.75 -3.75t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -3.75t + t2 = 0.75 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 0.75 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 0.75 + 3.515625 Combine like terms: 0.75 + 3.515625 = 4.265625 3.515625 + -3.75t + t2 = 4.265625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (t + -1.875) equal to 2.065338955 and -2.065338955.Subproblem 1
t + -1.875 = 2.065338955 Simplifying t + -1.875 = 2.065338955 Reorder the terms: -1.875 + t = 2.065338955 Solving -1.875 + t = 2.065338955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 2.065338955 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 2.065338955 + 1.875 t = 2.065338955 + 1.875 Combine like terms: 2.065338955 + 1.875 = 3.940338955 t = 3.940338955 Simplifying t = 3.940338955Subproblem 2
t + -1.875 = -2.065338955 Simplifying t + -1.875 = -2.065338955 Reorder the terms: -1.875 + t = -2.065338955 Solving -1.875 + t = -2.065338955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -2.065338955 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -2.065338955 + 1.875 t = -2.065338955 + 1.875 Combine like terms: -2.065338955 + 1.875 = -0.190338955 t = -0.190338955 Simplifying t = -0.190338955Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.940338955, -0.190338955}Solution
t = {3.940338955, -0.190338955}
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