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Simplifying -16t2 + -15t + 112 = 0 Reorder the terms: 112 + -15t + -16t2 = 0 Solving 112 + -15t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -7 + 0.9375t + t2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.9375t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + 0.9375t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.9375t + t2 = 0 + 7 0.9375t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.9375t + t2 = 7 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 = 7 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 7 + 0.2197265625 Combine like terms: 7 + 0.2197265625 = 7.2197265625 0.2197265625 + 0.9375t + t2 = 7.2197265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 7.2197265625 Calculate the square root of the right side: 2.686954887 Break this problem into two subproblems by setting (t + 0.46875) equal to 2.686954887 and -2.686954887.Subproblem 1
t + 0.46875 = 2.686954887 Simplifying t + 0.46875 = 2.686954887 Reorder the terms: 0.46875 + t = 2.686954887 Solving 0.46875 + t = 2.686954887 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 = 2.686954887 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 2.686954887 + -0.46875 t = 2.686954887 + -0.46875 Combine like terms: 2.686954887 + -0.46875 = 2.218204887 t = 2.218204887 Simplifying t = 2.218204887Subproblem 2
t + 0.46875 = -2.686954887 Simplifying t + 0.46875 = -2.686954887 Reorder the terms: 0.46875 + t = -2.686954887 Solving 0.46875 + t = -2.686954887 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 = -2.686954887 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -2.686954887 + -0.46875 t = -2.686954887 + -0.46875 Combine like terms: -2.686954887 + -0.46875 = -3.155704887 t = -3.155704887 Simplifying t = -3.155704887Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.218204887, -3.155704887}
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