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Simplifying -10t2 + 44t + 100 = 0 Reorder the terms: 100 + 44t + -10t2 = 0 Solving 100 + 44t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 22t + -5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 22t + -5t2)' equal to zero and attempt to solve: Simplifying 50 + 22t + -5t2 = 0 Solving 50 + 22t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10 + -4.4t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4.4t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -4.4t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4.4t + t2 = 0 + 10 -4.4t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4.4t + t2 = 10 The t term is -4.4t. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4t + 4.84 + t2 = 10 + 4.84 Reorder the terms: 4.84 + -4.4t + t2 = 10 + 4.84 Combine like terms: 10 + 4.84 = 14.84 4.84 + -4.4t + t2 = 14.84 Factor a perfect square on the left side: (t + -2.2)(t + -2.2) = 14.84 Calculate the square root of the right side: 3.852272057 Break this problem into two subproblems by setting (t + -2.2) equal to 3.852272057 and -3.852272057.Subproblem 1
t + -2.2 = 3.852272057 Simplifying t + -2.2 = 3.852272057 Reorder the terms: -2.2 + t = 3.852272057 Solving -2.2 + t = 3.852272057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + t = 3.852272057 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + t = 3.852272057 + 2.2 t = 3.852272057 + 2.2 Combine like terms: 3.852272057 + 2.2 = 6.052272057 t = 6.052272057 Simplifying t = 6.052272057Subproblem 2
t + -2.2 = -3.852272057 Simplifying t + -2.2 = -3.852272057 Reorder the terms: -2.2 + t = -3.852272057 Solving -2.2 + t = -3.852272057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + t = -3.852272057 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + t = -3.852272057 + 2.2 t = -3.852272057 + 2.2 Combine like terms: -3.852272057 + 2.2 = -1.652272057 t = -1.652272057 Simplifying t = -1.652272057Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.052272057, -1.652272057}Solution
t = {6.052272057, -1.652272057}
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