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Simplifying 16t2 + -256t = 200 Reorder the terms: -256t + 16t2 = 200 Solving -256t + 16t2 = 200 Solving for variable 't'. Reorder the terms: -200 + -256t + 16t2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -256t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + -32t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-25 + -32t + 2t2)' equal to zero and attempt to solve: Simplifying -25 + -32t + 2t2 = 0 Solving -25 + -32t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -16t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -16t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -16t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -16t + t2 = 0 + 12.5 -16t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -16t + t2 = 12.5 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 12.5 + 64 Reorder the terms: 64 + -16t + t2 = 12.5 + 64 Combine like terms: 12.5 + 64 = 76.5 64 + -16t + t2 = 76.5 Factor a perfect square on the left side: (t + -8)(t + -8) = 76.5 Calculate the square root of the right side: 8.746427842 Break this problem into two subproblems by setting (t + -8) equal to 8.746427842 and -8.746427842.Subproblem 1
t + -8 = 8.746427842 Simplifying t + -8 = 8.746427842 Reorder the terms: -8 + t = 8.746427842 Solving -8 + t = 8.746427842 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 8.746427842 + 8 Combine like terms: -8 + 8 = 0 0 + t = 8.746427842 + 8 t = 8.746427842 + 8 Combine like terms: 8.746427842 + 8 = 16.746427842 t = 16.746427842 Simplifying t = 16.746427842Subproblem 2
t + -8 = -8.746427842 Simplifying t + -8 = -8.746427842 Reorder the terms: -8 + t = -8.746427842 Solving -8 + t = -8.746427842 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -8.746427842 + 8 Combine like terms: -8 + 8 = 0 0 + t = -8.746427842 + 8 t = -8.746427842 + 8 Combine like terms: -8.746427842 + 8 = -0.746427842 t = -0.746427842 Simplifying t = -0.746427842Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.746427842, -0.746427842}Solution
t = {16.746427842, -0.746427842}
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