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Simplifying 14410 = 16t + 16t2 Solving 14410 = 16t + 16t2 Solving for variable 't'. Reorder the terms: 14410 + -16t + -16t2 = 16t + -16t + 16t2 + -16t2 Combine like terms: 16t + -16t = 0 14410 + -16t + -16t2 = 0 + 16t2 + -16t2 14410 + -16t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 14410 + -16t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7205 + -8t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7205 + -8t + -8t2)' equal to zero and attempt to solve: Simplifying 7205 + -8t + -8t2 = 0 Solving 7205 + -8t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -900.625 + t + t2 = 0 Move the constant term to the right: Add '900.625' to each side of the equation. -900.625 + t + 900.625 + t2 = 0 + 900.625 Reorder the terms: -900.625 + 900.625 + t + t2 = 0 + 900.625 Combine like terms: -900.625 + 900.625 = 0.000 0.000 + t + t2 = 0 + 900.625 t + t2 = 0 + 900.625 Combine like terms: 0 + 900.625 = 900.625 t + t2 = 900.625 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 = 900.625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 900.625 + 0.25 Combine like terms: 900.625 + 0.25 = 900.875 1.25 + t2 = 900.875 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 900.875 Calculate the square root of the right side: 30.01457979 Break this problem into two subproblems by setting (t + 0.5) equal to 30.01457979 and -30.01457979.Subproblem 1
t + 0.5 = 30.01457979 Simplifying t + 0.5 = 30.01457979 Reorder the terms: 0.5 + t = 30.01457979 Solving 0.5 + t = 30.01457979 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 = 30.01457979 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 30.01457979 + -0.5 t = 30.01457979 + -0.5 Combine like terms: 30.01457979 + -0.5 = 29.51457979 t = 29.51457979 Simplifying t = 29.51457979Subproblem 2
t + 0.5 = -30.01457979 Simplifying t + 0.5 = -30.01457979 Reorder the terms: 0.5 + t = -30.01457979 Solving 0.5 + t = -30.01457979 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 = -30.01457979 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -30.01457979 + -0.5 t = -30.01457979 + -0.5 Combine like terms: -30.01457979 + -0.5 = -30.51457979 t = -30.51457979 Simplifying t = -30.51457979Solution
The solution to the problem is based on the solutions from the subproblems. t = {29.51457979, -30.51457979}Solution
t = {29.51457979, -30.51457979}
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