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Simplifying t2 + 13t = -17 Reorder the terms: 13t + t2 = -17 Solving 13t + t2 = -17 Solving for variable 't'. Reorder the terms: 17 + 13t + t2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 13t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 13t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + 13t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 13t + t2 = 0 + -17 13t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 13t + t2 = -17 The t term is 13t. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13t + 42.25 + t2 = -17 + 42.25 Reorder the terms: 42.25 + 13t + t2 = -17 + 42.25 Combine like terms: -17 + 42.25 = 25.25 42.25 + 13t + t2 = 25.25 Factor a perfect square on the left side: (t + 6.5)(t + 6.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (t + 6.5) equal to 5.024937811 and -5.024937811.Subproblem 1
t + 6.5 = 5.024937811 Simplifying t + 6.5 = 5.024937811 Reorder the terms: 6.5 + t = 5.024937811 Solving 6.5 + t = 5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + t = 5.024937811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = 5.024937811 + -6.5 t = 5.024937811 + -6.5 Combine like terms: 5.024937811 + -6.5 = -1.475062189 t = -1.475062189 Simplifying t = -1.475062189Subproblem 2
t + 6.5 = -5.024937811 Simplifying t + 6.5 = -5.024937811 Reorder the terms: 6.5 + t = -5.024937811 Solving 6.5 + t = -5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + t = -5.024937811 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + t = -5.024937811 + -6.5 t = -5.024937811 + -6.5 Combine like terms: -5.024937811 + -6.5 = -11.524937811 t = -11.524937811 Simplifying t = -11.524937811Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.475062189, -11.524937811}
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