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Simplifying -25t2 + 200t + 400 = 0 Reorder the terms: 400 + 200t + -25t2 = 0 Solving 400 + 200t + -25t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '25'. 25(16 + 8t + -1t2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(16 + 8t + -1t2)' equal to zero and attempt to solve: Simplifying 16 + 8t + -1t2 = 0 Solving 16 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -8t + t2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -8t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -8t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8t + t2 = 0 + 16 -8t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8t + t2 = 16 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 16 + 16 Reorder the terms: 16 + -8t + t2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8t + t2 = 32 Factor a perfect square on the left side: (t + -4)(t + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (t + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
t + -4 = 5.656854249 Simplifying t + -4 = 5.656854249 Reorder the terms: -4 + t = 5.656854249 Solving -4 + t = 5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.656854249 + 4 t = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 t = 9.656854249 Simplifying t = 9.656854249Subproblem 2
t + -4 = -5.656854249 Simplifying t + -4 = -5.656854249 Reorder the terms: -4 + t = -5.656854249 Solving -4 + t = -5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.656854249 + 4 t = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 t = -1.656854249 Simplifying t = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.656854249, -1.656854249}Solution
t = {9.656854249, -1.656854249}
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