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Simplifying 0 = 16t2 + 484t + 521 Reorder the terms: 0 = 521 + 484t + 16t2 Solving 0 = 521 + 484t + 16t2 Solving for variable 't'. Combine like terms: 0 + -521 = -521 -521 + -484t + -16t2 = 521 + 484t + 16t2 + -521 + -484t + -16t2 Reorder the terms: -521 + -484t + -16t2 = 521 + -521 + 484t + -484t + 16t2 + -16t2 Combine like terms: 521 + -521 = 0 -521 + -484t + -16t2 = 0 + 484t + -484t + 16t2 + -16t2 -521 + -484t + -16t2 = 484t + -484t + 16t2 + -16t2 Combine like terms: 484t + -484t = 0 -521 + -484t + -16t2 = 0 + 16t2 + -16t2 -521 + -484t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -521 + -484t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(521 + 484t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(521 + 484t + 16t2)' equal to zero and attempt to solve: Simplifying 521 + 484t + 16t2 = 0 Solving 521 + 484t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 32.5625 + 30.25t + t2 = 0 Move the constant term to the right: Add '-32.5625' to each side of the equation. 32.5625 + 30.25t + -32.5625 + t2 = 0 + -32.5625 Reorder the terms: 32.5625 + -32.5625 + 30.25t + t2 = 0 + -32.5625 Combine like terms: 32.5625 + -32.5625 = 0.0000 0.0000 + 30.25t + t2 = 0 + -32.5625 30.25t + t2 = 0 + -32.5625 Combine like terms: 0 + -32.5625 = -32.5625 30.25t + t2 = -32.5625 The t term is 30.25t. Take half its coefficient (15.125). Square it (228.765625) and add it to both sides. Add '228.765625' to each side of the equation. 30.25t + 228.765625 + t2 = -32.5625 + 228.765625 Reorder the terms: 228.765625 + 30.25t + t2 = -32.5625 + 228.765625 Combine like terms: -32.5625 + 228.765625 = 196.203125 228.765625 + 30.25t + t2 = 196.203125 Factor a perfect square on the left side: (t + 15.125)(t + 15.125) = 196.203125 Calculate the square root of the right side: 14.007252586 Break this problem into two subproblems by setting (t + 15.125) equal to 14.007252586 and -14.007252586.Subproblem 1
t + 15.125 = 14.007252586 Simplifying t + 15.125 = 14.007252586 Reorder the terms: 15.125 + t = 14.007252586 Solving 15.125 + t = 14.007252586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15.125' to each side of the equation. 15.125 + -15.125 + t = 14.007252586 + -15.125 Combine like terms: 15.125 + -15.125 = 0.000 0.000 + t = 14.007252586 + -15.125 t = 14.007252586 + -15.125 Combine like terms: 14.007252586 + -15.125 = -1.117747414 t = -1.117747414 Simplifying t = -1.117747414Subproblem 2
t + 15.125 = -14.007252586 Simplifying t + 15.125 = -14.007252586 Reorder the terms: 15.125 + t = -14.007252586 Solving 15.125 + t = -14.007252586 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15.125' to each side of the equation. 15.125 + -15.125 + t = -14.007252586 + -15.125 Combine like terms: 15.125 + -15.125 = 0.000 0.000 + t = -14.007252586 + -15.125 t = -14.007252586 + -15.125 Combine like terms: -14.007252586 + -15.125 = -29.132252586 t = -29.132252586 Simplifying t = -29.132252586Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.117747414, -29.132252586}Solution
t = {-1.117747414, -29.132252586}
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