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Simplifying -16t2 + 153t + 15 = 0 Reorder the terms: 15 + 153t + -16t2 = 0 Solving 15 + 153t + -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'. -0.9375 + -9.5625t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -9.5625t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -9.5625t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -9.5625t + t2 = 0 + 0.9375 -9.5625t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -9.5625t + t2 = 0.9375 The t term is -9.5625t. Take half its coefficient (-4.78125). Square it (22.86035156) and add it to both sides. Add '22.86035156' to each side of the equation. -9.5625t + 22.86035156 + t2 = 0.9375 + 22.86035156 Reorder the terms: 22.86035156 + -9.5625t + t2 = 0.9375 + 22.86035156 Combine like terms: 0.9375 + 22.86035156 = 23.79785156 22.86035156 + -9.5625t + t2 = 23.79785156 Factor a perfect square on the left side: (t + -4.78125)(t + -4.78125) = 23.79785156 Calculate the square root of the right side: 4.878304168 Break this problem into two subproblems by setting (t + -4.78125) equal to 4.878304168 and -4.878304168.Subproblem 1
t + -4.78125 = 4.878304168 Simplifying t + -4.78125 = 4.878304168 Reorder the terms: -4.78125 + t = 4.878304168 Solving -4.78125 + t = 4.878304168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.78125' to each side of the equation. -4.78125 + 4.78125 + t = 4.878304168 + 4.78125 Combine like terms: -4.78125 + 4.78125 = 0.00000 0.00000 + t = 4.878304168 + 4.78125 t = 4.878304168 + 4.78125 Combine like terms: 4.878304168 + 4.78125 = 9.659554168 t = 9.659554168 Simplifying t = 9.659554168Subproblem 2
t + -4.78125 = -4.878304168 Simplifying t + -4.78125 = -4.878304168 Reorder the terms: -4.78125 + t = -4.878304168 Solving -4.78125 + t = -4.878304168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.78125' to each side of the equation. -4.78125 + 4.78125 + t = -4.878304168 + 4.78125 Combine like terms: -4.78125 + 4.78125 = 0.00000 0.00000 + t = -4.878304168 + 4.78125 t = -4.878304168 + 4.78125 Combine like terms: -4.878304168 + 4.78125 = -0.097054168 t = -0.097054168 Simplifying t = -0.097054168Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.659554168, -0.097054168}
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