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Simplifying -16t2 + 30t + 500 = 0 Reorder the terms: 500 + 30t + -16t2 = 0 Solving 500 + 30t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(250 + 15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(250 + 15t + -8t2)' equal to zero and attempt to solve: Simplifying 250 + 15t + -8t2 = 0 Solving 250 + 15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -31.25 + -1.875t + t2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -1.875t + 31.25 + t2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -1.875t + t2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -1.875t + t2 = 0 + 31.25 -1.875t + t2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -1.875t + t2 = 31.25 The t term is -1.875t. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875t + 0.87890625 + t2 = 31.25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 31.25 + 0.87890625 Combine like terms: 31.25 + 0.87890625 = 32.12890625 0.87890625 + -1.875t + t2 = 32.12890625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 32.12890625 Calculate the square root of the right side: 5.668236609 Break this problem into two subproblems by setting (t + -0.9375) equal to 5.668236609 and -5.668236609.Subproblem 1
t + -0.9375 = 5.668236609 Simplifying t + -0.9375 = 5.668236609 Reorder the terms: -0.9375 + t = 5.668236609 Solving -0.9375 + t = 5.668236609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = 5.668236609 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 5.668236609 + 0.9375 t = 5.668236609 + 0.9375 Combine like terms: 5.668236609 + 0.9375 = 6.605736609 t = 6.605736609 Simplifying t = 6.605736609Subproblem 2
t + -0.9375 = -5.668236609 Simplifying t + -0.9375 = -5.668236609 Reorder the terms: -0.9375 + t = -5.668236609 Solving -0.9375 + t = -5.668236609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + t = -5.668236609 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -5.668236609 + 0.9375 t = -5.668236609 + 0.9375 Combine like terms: -5.668236609 + 0.9375 = -4.730736609 t = -4.730736609 Simplifying t = -4.730736609Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.605736609, -4.730736609}Solution
t = {6.605736609, -4.730736609}
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