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Simplifying -0.7t2 + 16.8t = 66.5 Reorder the terms: 16.8t + -0.7t2 = 66.5 Solving 16.8t + -0.7t2 = 66.5 Solving for variable 't'. Reorder the terms: -66.5 + 16.8t + -0.7t2 = 66.5 + -66.5 Combine like terms: 66.5 + -66.5 = 0.0 -66.5 + 16.8t + -0.7t2 = 0.0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. 95 + -24t + t2 = 0 Move the constant term to the right: Add '-95' to each side of the equation. 95 + -24t + -95 + t2 = 0 + -95 Reorder the terms: 95 + -95 + -24t + t2 = 0 + -95 Combine like terms: 95 + -95 = 0 0 + -24t + t2 = 0 + -95 -24t + t2 = 0 + -95 Combine like terms: 0 + -95 = -95 -24t + t2 = -95 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -95 + 144 Reorder the terms: 144 + -24t + t2 = -95 + 144 Combine like terms: -95 + 144 = 49 144 + -24t + t2 = 49 Factor a perfect square on the left side: (t + -12)(t + -12) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (t + -12) equal to 7 and -7.Subproblem 1
t + -12 = 7 Simplifying t + -12 = 7 Reorder the terms: -12 + t = 7 Solving -12 + t = 7 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 7 + 12 Combine like terms: -12 + 12 = 0 0 + t = 7 + 12 t = 7 + 12 Combine like terms: 7 + 12 = 19 t = 19 Simplifying t = 19Subproblem 2
t + -12 = -7 Simplifying t + -12 = -7 Reorder the terms: -12 + t = -7 Solving -12 + t = -7 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -7 + 12 Combine like terms: -12 + 12 = 0 0 + t = -7 + 12 t = -7 + 12 Combine like terms: -7 + 12 = 5 t = 5 Simplifying t = 5Solution
The solution to the problem is based on the solutions from the subproblems. t = {19, 5}
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