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Simplifying 400 = -16t2 + 400t Reorder the terms: 400 = 400t + -16t2 Solving 400 = 400t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -400t + 16t2 = 400t + -400t + -16t2 + 16t2 Combine like terms: 400t + -400t = 0 400 + -400t + 16t2 = 0 + -16t2 + 16t2 400 + -400t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -400t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(25 + -25t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(25 + -25t + t2)' equal to zero and attempt to solve: Simplifying 25 + -25t + t2 = 0 Solving 25 + -25t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -25t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -25t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -25t + t2 = 0 + -25 -25t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -25t + t2 = -25 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -25 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -25 + 156.25 Combine like terms: -25 + 156.25 = 131.25 156.25 + -25t + t2 = 131.25 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (t + -12.5) equal to 11.456439237 and -11.456439237.Subproblem 1
t + -12.5 = 11.456439237 Simplifying t + -12.5 = 11.456439237 Reorder the terms: -12.5 + t = 11.456439237 Solving -12.5 + t = 11.456439237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 11.456439237 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 11.456439237 + 12.5 t = 11.456439237 + 12.5 Combine like terms: 11.456439237 + 12.5 = 23.956439237 t = 23.956439237 Simplifying t = 23.956439237Subproblem 2
t + -12.5 = -11.456439237 Simplifying t + -12.5 = -11.456439237 Reorder the terms: -12.5 + t = -11.456439237 Solving -12.5 + t = -11.456439237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -11.456439237 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -11.456439237 + 12.5 t = -11.456439237 + 12.5 Combine like terms: -11.456439237 + 12.5 = 1.043560763 t = 1.043560763 Simplifying t = 1.043560763Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.956439237, 1.043560763}Solution
t = {23.956439237, 1.043560763}
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