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Simplifying -16t2 + 800t + 500 = 0 Reorder the terms: 500 + 800t + -16t2 = 0 Solving 500 + 800t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(125 + 200t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(125 + 200t + -4t2)' equal to zero and attempt to solve: Simplifying 125 + 200t + -4t2 = 0 Solving 125 + 200t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -31.25 + -50t + t2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -50t + 31.25 + t2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -50t + t2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -50t + t2 = 0 + 31.25 -50t + t2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -50t + t2 = 31.25 The t term is -50t. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50t + 625 + t2 = 31.25 + 625 Reorder the terms: 625 + -50t + t2 = 31.25 + 625 Combine like terms: 31.25 + 625 = 656.25 625 + -50t + t2 = 656.25 Factor a perfect square on the left side: (t + -25)(t + -25) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (t + -25) equal to 25.617376915 and -25.617376915.Subproblem 1
t + -25 = 25.617376915 Simplifying t + -25 = 25.617376915 Reorder the terms: -25 + t = 25.617376915 Solving -25 + t = 25.617376915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = 25.617376915 + 25 Combine like terms: -25 + 25 = 0 0 + t = 25.617376915 + 25 t = 25.617376915 + 25 Combine like terms: 25.617376915 + 25 = 50.617376915 t = 50.617376915 Simplifying t = 50.617376915Subproblem 2
t + -25 = -25.617376915 Simplifying t + -25 = -25.617376915 Reorder the terms: -25 + t = -25.617376915 Solving -25 + t = -25.617376915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = -25.617376915 + 25 Combine like terms: -25 + 25 = 0 0 + t = -25.617376915 + 25 t = -25.617376915 + 25 Combine like terms: -25.617376915 + 25 = -0.617376915 t = -0.617376915 Simplifying t = -0.617376915Solution
The solution to the problem is based on the solutions from the subproblems. t = {50.617376915, -0.617376915}Solution
t = {50.617376915, -0.617376915}
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