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Simplifying -1t2 + 31t + -145 = 0 Reorder the terms: -145 + 31t + -1t2 = 0 Solving -145 + 31t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 145 + -31t + t2 = 0 Move the constant term to the right: Add '-145' to each side of the equation. 145 + -31t + -145 + t2 = 0 + -145 Reorder the terms: 145 + -145 + -31t + t2 = 0 + -145 Combine like terms: 145 + -145 = 0 0 + -31t + t2 = 0 + -145 -31t + t2 = 0 + -145 Combine like terms: 0 + -145 = -145 -31t + t2 = -145 The t term is -31t. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31t + 240.25 + t2 = -145 + 240.25 Reorder the terms: 240.25 + -31t + t2 = -145 + 240.25 Combine like terms: -145 + 240.25 = 95.25 240.25 + -31t + t2 = 95.25 Factor a perfect square on the left side: (t + -15.5)(t + -15.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (t + -15.5) equal to 9.759610648 and -9.759610648.Subproblem 1
t + -15.5 = 9.759610648 Simplifying t + -15.5 = 9.759610648 Reorder the terms: -15.5 + t = 9.759610648 Solving -15.5 + t = 9.759610648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = 9.759610648 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = 9.759610648 + 15.5 t = 9.759610648 + 15.5 Combine like terms: 9.759610648 + 15.5 = 25.259610648 t = 25.259610648 Simplifying t = 25.259610648Subproblem 2
t + -15.5 = -9.759610648 Simplifying t + -15.5 = -9.759610648 Reorder the terms: -15.5 + t = -9.759610648 Solving -15.5 + t = -9.759610648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = -9.759610648 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = -9.759610648 + 15.5 t = -9.759610648 + 15.5 Combine like terms: -9.759610648 + 15.5 = 5.740389352 t = 5.740389352 Simplifying t = 5.740389352Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.259610648, 5.740389352}
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