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Simplifying -16t2 + -15t + 15 = 6 Reorder the terms: 15 + -15t + -16t2 = 6 Solving 15 + -15t + -16t2 = 6 Solving for variable 't'. Reorder the terms: 15 + -6 + -15t + -16t2 = 6 + -6 Combine like terms: 15 + -6 = 9 9 + -15t + -16t2 = 6 + -6 Combine like terms: 6 + -6 = 0 9 + -15t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5625 + 0.9375t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 0.9375t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 0.9375t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 0.9375t + t2 = 0 + 0.5625 0.9375t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 0.9375t + t2 = 0.5625 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 = 0.5625 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 0.5625 + 0.2197265625 Combine like terms: 0.5625 + 0.2197265625 = 0.7822265625 0.2197265625 + 0.9375t + t2 = 0.7822265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 0.7822265625 Calculate the square root of the right side: 0.884435731 Break this problem into two subproblems by setting (t + 0.46875) equal to 0.884435731 and -0.884435731.Subproblem 1
t + 0.46875 = 0.884435731 Simplifying t + 0.46875 = 0.884435731 Reorder the terms: 0.46875 + t = 0.884435731 Solving 0.46875 + t = 0.884435731 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 = 0.884435731 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 0.884435731 + -0.46875 t = 0.884435731 + -0.46875 Combine like terms: 0.884435731 + -0.46875 = 0.415685731 t = 0.415685731 Simplifying t = 0.415685731Subproblem 2
t + 0.46875 = -0.884435731 Simplifying t + 0.46875 = -0.884435731 Reorder the terms: 0.46875 + t = -0.884435731 Solving 0.46875 + t = -0.884435731 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 = -0.884435731 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -0.884435731 + -0.46875 t = -0.884435731 + -0.46875 Combine like terms: -0.884435731 + -0.46875 = -1.353185731 t = -1.353185731 Simplifying t = -1.353185731Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.415685731, -1.353185731}
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