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Simplifying -1(16t2 + -16t + -464) = 0 Reorder the terms: -1(-464 + -16t + 16t2) = 0 (-464 * -1 + -16t * -1 + 16t2 * -1) = 0 (464 + 16t + -16t2) = 0 Solving 464 + 16t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(29 + t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(29 + t + -1t2)' equal to zero and attempt to solve: Simplifying 29 + t + -1t2 = 0 Solving 29 + t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + -1t + t2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + -1t + 29 + t2 = 0 + 29 Reorder the terms: -29 + 29 + -1t + t2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1t + t2 = 0 + 29 -1t + t2 = 0 + 29 Combine like terms: 0 + 29 = 29 -1t + t2 = 29 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. -1t + 0.25 + t2 = 29 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 0.25 + -1t + t2 = 29.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (t + 0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
t + 0.5 = 5.408326913 Simplifying t + 0.5 = 5.408326913 Reorder the terms: 0.5 + t = 5.408326913 Solving 0.5 + t = 5.408326913 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 = 5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 5.408326913 + -0.5 t = 5.408326913 + -0.5 Combine like terms: 5.408326913 + -0.5 = 4.908326913 t = 4.908326913 Simplifying t = 4.908326913Subproblem 2
t + 0.5 = -5.408326913 Simplifying t + 0.5 = -5.408326913 Reorder the terms: 0.5 + t = -5.408326913 Solving 0.5 + t = -5.408326913 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 = -5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -5.408326913 + -0.5 t = -5.408326913 + -0.5 Combine like terms: -5.408326913 + -0.5 = -5.908326913 t = -5.908326913 Simplifying t = -5.908326913Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.908326913, -5.908326913}Solution
t = {4.908326913, -5.908326913}
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