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Simplifying 0 = -16t2 + 15t + 30 Reorder the terms: 0 = 30 + 15t + -16t2 Solving 0 = 30 + 15t + -16t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + -15t + 16t2 = 30 + 15t + -16t2 + -30 + -15t + 16t2 Reorder the terms: -30 + -15t + 16t2 = 30 + -30 + 15t + -15t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 -30 + -15t + 16t2 = 0 + 15t + -15t + -16t2 + 16t2 -30 + -15t + 16t2 = 15t + -15t + -16t2 + 16t2 Combine like terms: 15t + -15t = 0 -30 + -15t + 16t2 = 0 + -16t2 + 16t2 -30 + -15t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.875 + -0.9375t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -0.9375t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -0.9375t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -0.9375t + t2 = 0 + 1.875 -0.9375t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -0.9375t + t2 = 1.875 The t term is -0.9375t. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375t + 0.2197265625 + t2 = 1.875 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 1.875 + 0.2197265625 Combine like terms: 1.875 + 0.2197265625 = 2.0947265625 0.2197265625 + -0.9375t + t2 = 2.0947265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 2.0947265625 Calculate the square root of the right side: 1.447317022 Break this problem into two subproblems by setting (t + -0.46875) equal to 1.447317022 and -1.447317022.Subproblem 1
t + -0.46875 = 1.447317022 Simplifying t + -0.46875 = 1.447317022 Reorder the terms: -0.46875 + t = 1.447317022 Solving -0.46875 + t = 1.447317022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = 1.447317022 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 1.447317022 + 0.46875 t = 1.447317022 + 0.46875 Combine like terms: 1.447317022 + 0.46875 = 1.916067022 t = 1.916067022 Simplifying t = 1.916067022Subproblem 2
t + -0.46875 = -1.447317022 Simplifying t + -0.46875 = -1.447317022 Reorder the terms: -0.46875 + t = -1.447317022 Solving -0.46875 + t = -1.447317022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = -1.447317022 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -1.447317022 + 0.46875 t = -1.447317022 + 0.46875 Combine like terms: -1.447317022 + 0.46875 = -0.978567022 t = -0.978567022 Simplifying t = -0.978567022Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.916067022, -0.978567022}
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