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Simplifying -16t2 + 25t + -7 = 0 Reorder the terms: -7 + 25t + -16t2 = 0 Solving -7 + 25t + -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'. 0.4375 + -1.5625t + t2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -1.5625t + -0.4375 + t2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -1.5625t + t2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -1.5625t + t2 = 0 + -0.4375 -1.5625t + t2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -1.5625t + t2 = -0.4375 The t term is -1.5625t. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625t + 0.6103515625 + t2 = -0.4375 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = -0.4375 + 0.6103515625 Combine like terms: -0.4375 + 0.6103515625 = 0.1728515625 0.6103515625 + -1.5625t + t2 = 0.1728515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 0.1728515625 Calculate the square root of the right side: 0.415754209 Break this problem into two subproblems by setting (t + -0.78125) equal to 0.415754209 and -0.415754209.Subproblem 1
t + -0.78125 = 0.415754209 Simplifying t + -0.78125 = 0.415754209 Reorder the terms: -0.78125 + t = 0.415754209 Solving -0.78125 + t = 0.415754209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 0.415754209 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 0.415754209 + 0.78125 t = 0.415754209 + 0.78125 Combine like terms: 0.415754209 + 0.78125 = 1.197004209 t = 1.197004209 Simplifying t = 1.197004209Subproblem 2
t + -0.78125 = -0.415754209 Simplifying t + -0.78125 = -0.415754209 Reorder the terms: -0.78125 + t = -0.415754209 Solving -0.78125 + t = -0.415754209 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -0.415754209 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -0.415754209 + 0.78125 t = -0.415754209 + 0.78125 Combine like terms: -0.415754209 + 0.78125 = 0.365495791 t = 0.365495791 Simplifying t = 0.365495791Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.197004209, 0.365495791}
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