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Simplifying 180 = -16t + 120t2 Solving 180 = -16t + 120t2 Solving for variable 't'. Reorder the terms: 180 + 16t + -120t2 = -16t + 16t + 120t2 + -120t2 Combine like terms: -16t + 16t = 0 180 + 16t + -120t2 = 0 + 120t2 + -120t2 180 + 16t + -120t2 = 120t2 + -120t2 Combine like terms: 120t2 + -120t2 = 0 180 + 16t + -120t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(45 + 4t + -30t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(45 + 4t + -30t2)' equal to zero and attempt to solve: Simplifying 45 + 4t + -30t2 = 0 Solving 45 + 4t + -30t2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. -1.5 + -0.1333333333t + t2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.1333333333t + 1.5 + t2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.1333333333t + t2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.1333333333t + t2 = 0.0 + 1.5 -0.1333333333t + t2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -0.1333333333t + t2 = 1.5 The t term is -0.1333333333t. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333t + 0.004444444442 + t2 = 1.5 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333t + t2 = 1.5 + 0.004444444442 Combine like terms: 1.5 + 0.004444444442 = 1.504444444442 0.004444444442 + -0.1333333333t + t2 = 1.504444444442 Factor a perfect square on the left side: (t + -0.06666666665)(t + -0.06666666665) = 1.504444444442 Calculate the square root of the right side: 1.226557966 Break this problem into two subproblems by setting (t + -0.06666666665) equal to 1.226557966 and -1.226557966.Subproblem 1
t + -0.06666666665 = 1.226557966 Simplifying t + -0.06666666665 = 1.226557966 Reorder the terms: -0.06666666665 + t = 1.226557966 Solving -0.06666666665 + t = 1.226557966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = 1.226557966 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = 1.226557966 + 0.06666666665 t = 1.226557966 + 0.06666666665 Combine like terms: 1.226557966 + 0.06666666665 = 1.29322463265 t = 1.29322463265 Simplifying t = 1.29322463265Subproblem 2
t + -0.06666666665 = -1.226557966 Simplifying t + -0.06666666665 = -1.226557966 Reorder the terms: -0.06666666665 + t = -1.226557966 Solving -0.06666666665 + t = -1.226557966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = -1.226557966 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = -1.226557966 + 0.06666666665 t = -1.226557966 + 0.06666666665 Combine like terms: -1.226557966 + 0.06666666665 = -1.15989129935 t = -1.15989129935 Simplifying t = -1.15989129935Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.29322463265, -1.15989129935}Solution
t = {1.29322463265, -1.15989129935}
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