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Simplifying 48 + -16t + -16t2 = 0 Solving 48 + -16t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(3 + -1t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -1t + -1t2)' equal to zero and attempt to solve: Simplifying 3 + -1t + -1t2 = 0 Solving 3 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t + t2 = 0 + 3 t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 t + t2 = 3 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 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 1.25 + t2 = 3.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (t + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
t + 0.5 = 1.802775638 Simplifying t + 0.5 = 1.802775638 Reorder the terms: 0.5 + t = 1.802775638 Solving 0.5 + t = 1.802775638 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 = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.802775638 + -0.5 t = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 t = 1.302775638 Simplifying t = 1.302775638Subproblem 2
t + 0.5 = -1.802775638 Simplifying t + 0.5 = -1.802775638 Reorder the terms: 0.5 + t = -1.802775638 Solving 0.5 + t = -1.802775638 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 = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.802775638 + -0.5 t = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 t = -2.302775638 Simplifying t = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.302775638, -2.302775638}Solution
t = {1.302775638, -2.302775638}
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