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Simplifying -16t2 + 60t + 60 = 0 Reorder the terms: 60 + 60t + -16t2 = 0 Solving 60 + 60t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 15t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + 15t + -4t2)' equal to zero and attempt to solve: Simplifying 15 + 15t + -4t2 = 0 Solving 15 + 15t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.75 + -3.75t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -3.75t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -3.75t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -3.75t + t2 = 0 + 3.75 -3.75t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -3.75t + t2 = 3.75 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 = 3.75 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 3.75 + 3.515625 Combine like terms: 3.75 + 3.515625 = 7.265625 3.515625 + -3.75t + t2 = 7.265625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 7.265625 Calculate the square root of the right side: 2.695482332 Break this problem into two subproblems by setting (t + -1.875) equal to 2.695482332 and -2.695482332.Subproblem 1
t + -1.875 = 2.695482332 Simplifying t + -1.875 = 2.695482332 Reorder the terms: -1.875 + t = 2.695482332 Solving -1.875 + t = 2.695482332 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 = 2.695482332 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 2.695482332 + 1.875 t = 2.695482332 + 1.875 Combine like terms: 2.695482332 + 1.875 = 4.570482332 t = 4.570482332 Simplifying t = 4.570482332Subproblem 2
t + -1.875 = -2.695482332 Simplifying t + -1.875 = -2.695482332 Reorder the terms: -1.875 + t = -2.695482332 Solving -1.875 + t = -2.695482332 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 = -2.695482332 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -2.695482332 + 1.875 t = -2.695482332 + 1.875 Combine like terms: -2.695482332 + 1.875 = -0.820482332 t = -0.820482332 Simplifying t = -0.820482332Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.570482332, -0.820482332}Solution
t = {4.570482332, -0.820482332}
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