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Simplifying -16t2 + 112t + 6 = 25 Reorder the terms: 6 + 112t + -16t2 = 25 Solving 6 + 112t + -16t2 = 25 Solving for variable 't'. Reorder the terms: 6 + -25 + 112t + -16t2 = 25 + -25 Combine like terms: 6 + -25 = -19 -19 + 112t + -16t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -19 + 112t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.1875 + -7t + t2 = 0 Move the constant term to the right: Add '-1.1875' to each side of the equation. 1.1875 + -7t + -1.1875 + t2 = 0 + -1.1875 Reorder the terms: 1.1875 + -1.1875 + -7t + t2 = 0 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + -7t + t2 = 0 + -1.1875 -7t + t2 = 0 + -1.1875 Combine like terms: 0 + -1.1875 = -1.1875 -7t + t2 = -1.1875 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -1.1875 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -1.1875 + 12.25 Combine like terms: -1.1875 + 12.25 = 11.0625 12.25 + -7t + t2 = 11.0625 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (t + -3.5) equal to 3.326033674 and -3.326033674.Subproblem 1
t + -3.5 = 3.326033674 Simplifying t + -3.5 = 3.326033674 Reorder the terms: -3.5 + t = 3.326033674 Solving -3.5 + t = 3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.326033674 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.326033674 + 3.5 t = 3.326033674 + 3.5 Combine like terms: 3.326033674 + 3.5 = 6.826033674 t = 6.826033674 Simplifying t = 6.826033674Subproblem 2
t + -3.5 = -3.326033674 Simplifying t + -3.5 = -3.326033674 Reorder the terms: -3.5 + t = -3.326033674 Solving -3.5 + t = -3.326033674 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.326033674 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.326033674 + 3.5 t = -3.326033674 + 3.5 Combine like terms: -3.326033674 + 3.5 = 0.173966326 t = 0.173966326 Simplifying t = 0.173966326Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.826033674, 0.173966326}
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