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Simplifying -16t2 + 40t + 150 = 0 Reorder the terms: 150 + 40t + -16t2 = 0 Solving 150 + 40t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + 20t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + 20t + -8t2)' equal to zero and attempt to solve: Simplifying 75 + 20t + -8t2 = 0 Solving 75 + 20t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + -2.5t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + -2.5t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + -2.5t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + -2.5t + t2 = 0 + 9.375 -2.5t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 -2.5t + t2 = 9.375 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 9.375 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 9.375 + 1.5625 Combine like terms: 9.375 + 1.5625 = 10.9375 1.5625 + -2.5t + t2 = 10.9375 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 10.9375 Calculate the square root of the right side: 3.307189139 Break this problem into two subproblems by setting (t + -1.25) equal to 3.307189139 and -3.307189139.Subproblem 1
t + -1.25 = 3.307189139 Simplifying t + -1.25 = 3.307189139 Reorder the terms: -1.25 + t = 3.307189139 Solving -1.25 + t = 3.307189139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 3.307189139 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 3.307189139 + 1.25 t = 3.307189139 + 1.25 Combine like terms: 3.307189139 + 1.25 = 4.557189139 t = 4.557189139 Simplifying t = 4.557189139Subproblem 2
t + -1.25 = -3.307189139 Simplifying t + -1.25 = -3.307189139 Reorder the terms: -1.25 + t = -3.307189139 Solving -1.25 + t = -3.307189139 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -3.307189139 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -3.307189139 + 1.25 t = -3.307189139 + 1.25 Combine like terms: -3.307189139 + 1.25 = -2.057189139 t = -2.057189139 Simplifying t = -2.057189139Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.557189139, -2.057189139}Solution
t = {4.557189139, -2.057189139}
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