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Simplifying 10 = -16t2 + 72t + 20 Reorder the terms: 10 = 20 + 72t + -16t2 Solving 10 = 20 + 72t + -16t2 Solving for variable 't'. Combine like terms: 10 + -20 = -10 -10 + -72t + 16t2 = 20 + 72t + -16t2 + -20 + -72t + 16t2 Reorder the terms: -10 + -72t + 16t2 = 20 + -20 + 72t + -72t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 -10 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2 -10 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2 Combine like terms: 72t + -72t = 0 -10 + -72t + 16t2 = 0 + -16t2 + 16t2 -10 + -72t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -72t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -36t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -36t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -36t + 8t2 = 0 Solving -5 + -36t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -4.5t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -4.5t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -4.5t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -4.5t + t2 = 0 + 0.625 -4.5t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -4.5t + t2 = 0.625 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 0.625 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 0.625 + 5.0625 Combine like terms: 0.625 + 5.0625 = 5.6875 5.0625 + -4.5t + t2 = 5.6875 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 5.6875 Calculate the square root of the right side: 2.384848004 Break this problem into two subproblems by setting (t + -2.25) equal to 2.384848004 and -2.384848004.Subproblem 1
t + -2.25 = 2.384848004 Simplifying t + -2.25 = 2.384848004 Reorder the terms: -2.25 + t = 2.384848004 Solving -2.25 + t = 2.384848004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 2.384848004 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.384848004 + 2.25 t = 2.384848004 + 2.25 Combine like terms: 2.384848004 + 2.25 = 4.634848004 t = 4.634848004 Simplifying t = 4.634848004Subproblem 2
t + -2.25 = -2.384848004 Simplifying t + -2.25 = -2.384848004 Reorder the terms: -2.25 + t = -2.384848004 Solving -2.25 + t = -2.384848004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -2.384848004 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.384848004 + 2.25 t = -2.384848004 + 2.25 Combine like terms: -2.384848004 + 2.25 = -0.134848004 t = -0.134848004 Simplifying t = -0.134848004Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.634848004, -0.134848004}Solution
t = {4.634848004, -0.134848004}
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