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Simplifying 1050t = -16t2 + 1050 Reorder the terms: 1050t = 1050 + -16t2 Solving 1050t = 1050 + -16t2 Solving for variable 't'. Reorder the terms: -1050 + 1050t + 16t2 = 1050 + -16t2 + -1050 + 16t2 Reorder the terms: -1050 + 1050t + 16t2 = 1050 + -1050 + -16t2 + 16t2 Combine like terms: 1050 + -1050 = 0 -1050 + 1050t + 16t2 = 0 + -16t2 + 16t2 -1050 + 1050t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1050 + 1050t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-525 + 525t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-525 + 525t + 8t2)' equal to zero and attempt to solve: Simplifying -525 + 525t + 8t2 = 0 Solving -525 + 525t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -65.625 + 65.625t + t2 = 0 Move the constant term to the right: Add '65.625' to each side of the equation. -65.625 + 65.625t + 65.625 + t2 = 0 + 65.625 Reorder the terms: -65.625 + 65.625 + 65.625t + t2 = 0 + 65.625 Combine like terms: -65.625 + 65.625 = 0.000 0.000 + 65.625t + t2 = 0 + 65.625 65.625t + t2 = 0 + 65.625 Combine like terms: 0 + 65.625 = 65.625 65.625t + t2 = 65.625 The t term is 65.625t. Take half its coefficient (32.8125). Square it (1076.660156) and add it to both sides. Add '1076.660156' to each side of the equation. 65.625t + 1076.660156 + t2 = 65.625 + 1076.660156 Reorder the terms: 1076.660156 + 65.625t + t2 = 65.625 + 1076.660156 Combine like terms: 65.625 + 1076.660156 = 1142.285156 1076.660156 + 65.625t + t2 = 1142.285156 Factor a perfect square on the left side: (t + 32.8125)(t + 32.8125) = 1142.285156 Calculate the square root of the right side: 33.797709331 Break this problem into two subproblems by setting (t + 32.8125) equal to 33.797709331 and -33.797709331.Subproblem 1
t + 32.8125 = 33.797709331 Simplifying t + 32.8125 = 33.797709331 Reorder the terms: 32.8125 + t = 33.797709331 Solving 32.8125 + t = 33.797709331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-32.8125' to each side of the equation. 32.8125 + -32.8125 + t = 33.797709331 + -32.8125 Combine like terms: 32.8125 + -32.8125 = 0.0000 0.0000 + t = 33.797709331 + -32.8125 t = 33.797709331 + -32.8125 Combine like terms: 33.797709331 + -32.8125 = 0.985209331 t = 0.985209331 Simplifying t = 0.985209331Subproblem 2
t + 32.8125 = -33.797709331 Simplifying t + 32.8125 = -33.797709331 Reorder the terms: 32.8125 + t = -33.797709331 Solving 32.8125 + t = -33.797709331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-32.8125' to each side of the equation. 32.8125 + -32.8125 + t = -33.797709331 + -32.8125 Combine like terms: 32.8125 + -32.8125 = 0.0000 0.0000 + t = -33.797709331 + -32.8125 t = -33.797709331 + -32.8125 Combine like terms: -33.797709331 + -32.8125 = -66.610209331 t = -66.610209331 Simplifying t = -66.610209331Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.985209331, -66.610209331}Solution
t = {0.985209331, -66.610209331}
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