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Simplifying -16t2 + 150t + 30 = 20 Reorder the terms: 30 + 150t + -16t2 = 20 Solving 30 + 150t + -16t2 = 20 Solving for variable 't'. Reorder the terms: 30 + -20 + 150t + -16t2 = 20 + -20 Combine like terms: 30 + -20 = 10 10 + 150t + -16t2 = 20 + -20 Combine like terms: 20 + -20 = 0 10 + 150t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 75t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 75t + -8t2)' equal to zero and attempt to solve: Simplifying 5 + 75t + -8t2 = 0 Solving 5 + 75t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -9.375t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -9.375t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -9.375t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -9.375t + t2 = 0 + 0.625 -9.375t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -9.375t + t2 = 0.625 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = 0.625 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 0.625 + 21.97265625 Combine like terms: 0.625 + 21.97265625 = 22.59765625 21.97265625 + -9.375t + t2 = 22.59765625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 22.59765625 Calculate the square root of the right side: 4.753699217 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.753699217 and -4.753699217.Subproblem 1
t + -4.6875 = 4.753699217 Simplifying t + -4.6875 = 4.753699217 Reorder the terms: -4.6875 + t = 4.753699217 Solving -4.6875 + t = 4.753699217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 4.753699217 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.753699217 + 4.6875 t = 4.753699217 + 4.6875 Combine like terms: 4.753699217 + 4.6875 = 9.441199217 t = 9.441199217 Simplifying t = 9.441199217Subproblem 2
t + -4.6875 = -4.753699217 Simplifying t + -4.6875 = -4.753699217 Reorder the terms: -4.6875 + t = -4.753699217 Solving -4.6875 + t = -4.753699217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -4.753699217 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.753699217 + 4.6875 t = -4.753699217 + 4.6875 Combine like terms: -4.753699217 + 4.6875 = -0.066199217 t = -0.066199217 Simplifying t = -0.066199217Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.441199217, -0.066199217}Solution
t = {9.441199217, -0.066199217}
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