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Simplifying 50 = 16t2 + 16t Reorder the terms: 50 = 16t + 16t2 Solving 50 = 16t + 16t2 Solving for variable 't'. Reorder the terms: 50 + -16t + -16t2 = 16t + -16t + 16t2 + -16t2 Combine like terms: 16t + -16t = 0 50 + -16t + -16t2 = 0 + 16t2 + -16t2 50 + -16t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 50 + -16t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -8t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -8t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + -8t + -8t2 = 0 Solving 25 + -8t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t + t2 = 0 + 3.125 t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 t + t2 = 3.125 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 3.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 3.125 + 0.25 Combine like terms: 3.125 + 0.25 = 3.375 1.25 + t2 = 3.375 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (t + 0.5) equal to 1.837117307 and -1.837117307.Subproblem 1
t + 0.5 = 1.837117307 Simplifying t + 0.5 = 1.837117307 Reorder the terms: 0.5 + t = 1.837117307 Solving 0.5 + t = 1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.837117307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.837117307 + -0.5 t = 1.837117307 + -0.5 Combine like terms: 1.837117307 + -0.5 = 1.337117307 t = 1.337117307 Simplifying t = 1.337117307Subproblem 2
t + 0.5 = -1.837117307 Simplifying t + 0.5 = -1.837117307 Reorder the terms: 0.5 + t = -1.837117307 Solving 0.5 + t = -1.837117307 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.837117307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.837117307 + -0.5 t = -1.837117307 + -0.5 Combine like terms: -1.837117307 + -0.5 = -2.337117307 t = -2.337117307 Simplifying t = -2.337117307Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.337117307, -2.337117307}Solution
t = {1.337117307, -2.337117307}
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