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Simplifying -16t2 + 42t = 25 Reorder the terms: 42t + -16t2 = 25 Solving 42t + -16t2 = 25 Solving for variable 't'. Reorder the terms: -25 + 42t + -16t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 42t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.5625 + -2.625t + t2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + -2.625t + -1.5625 + t2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + -2.625t + t2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + -2.625t + t2 = 0 + -1.5625 -2.625t + t2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 -2.625t + t2 = -1.5625 The t term is -2.625t. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625t + 1.72265625 + t2 = -1.5625 + 1.72265625 Reorder the terms: 1.72265625 + -2.625t + t2 = -1.5625 + 1.72265625 Combine like terms: -1.5625 + 1.72265625 = 0.16015625 1.72265625 + -2.625t + t2 = 0.16015625 Factor a perfect square on the left side: (t + -1.3125)(t + -1.3125) = 0.16015625 Calculate the square root of the right side: 0.400195265 Break this problem into two subproblems by setting (t + -1.3125) equal to 0.400195265 and -0.400195265.Subproblem 1
t + -1.3125 = 0.400195265 Simplifying t + -1.3125 = 0.400195265 Reorder the terms: -1.3125 + t = 0.400195265 Solving -1.3125 + t = 0.400195265 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + t = 0.400195265 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + t = 0.400195265 + 1.3125 t = 0.400195265 + 1.3125 Combine like terms: 0.400195265 + 1.3125 = 1.712695265 t = 1.712695265 Simplifying t = 1.712695265Subproblem 2
t + -1.3125 = -0.400195265 Simplifying t + -1.3125 = -0.400195265 Reorder the terms: -1.3125 + t = -0.400195265 Solving -1.3125 + t = -0.400195265 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + t = -0.400195265 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + t = -0.400195265 + 1.3125 t = -0.400195265 + 1.3125 Combine like terms: -0.400195265 + 1.3125 = 0.912304735 t = 0.912304735 Simplifying t = 0.912304735Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.712695265, 0.912304735}
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