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Simplifying -16t2 + -23t + 100 = 0 Reorder the terms: 100 + -23t + -16t2 = 0 Solving 100 + -23t + -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'. -6.25 + 1.4375t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 1.4375t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 1.4375t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 1.4375t + t2 = 0 + 6.25 1.4375t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 1.4375t + t2 = 6.25 The t term is 1.4375t. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375t + 0.5166015625 + t2 = 6.25 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375t + t2 = 6.25 + 0.5166015625 Combine like terms: 6.25 + 0.5166015625 = 6.7666015625 0.5166015625 + 1.4375t + t2 = 6.7666015625 Factor a perfect square on the left side: (t + 0.71875)(t + 0.71875) = 6.7666015625 Calculate the square root of the right side: 2.601269221 Break this problem into two subproblems by setting (t + 0.71875) equal to 2.601269221 and -2.601269221.Subproblem 1
t + 0.71875 = 2.601269221 Simplifying t + 0.71875 = 2.601269221 Reorder the terms: 0.71875 + t = 2.601269221 Solving 0.71875 + t = 2.601269221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = 2.601269221 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = 2.601269221 + -0.71875 t = 2.601269221 + -0.71875 Combine like terms: 2.601269221 + -0.71875 = 1.882519221 t = 1.882519221 Simplifying t = 1.882519221Subproblem 2
t + 0.71875 = -2.601269221 Simplifying t + 0.71875 = -2.601269221 Reorder the terms: 0.71875 + t = -2.601269221 Solving 0.71875 + t = -2.601269221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + t = -2.601269221 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + t = -2.601269221 + -0.71875 t = -2.601269221 + -0.71875 Combine like terms: -2.601269221 + -0.71875 = -3.320019221 t = -3.320019221 Simplifying t = -3.320019221Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.882519221, -3.320019221}
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