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Simplifying t2 + 10t = -4 Reorder the terms: 10t + t2 = -4 Solving 10t + t2 = -4 Solving for variable 't'. Reorder the terms: 4 + 10t + t2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 10t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 10t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 10t + t2 = 0 + -4 10t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 10t + t2 = -4 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = -4 + 25 Reorder the terms: 25 + 10t + t2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + 10t + t2 = 21 Factor a perfect square on the left side: (t + 5)(t + 5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + 5) equal to 4.582575695 and -4.582575695.Subproblem 1
t + 5 = 4.582575695 Simplifying t + 5 = 4.582575695 Reorder the terms: 5 + t = 4.582575695 Solving 5 + t = 4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + t = 4.582575695 + -5 t = 4.582575695 + -5 Combine like terms: 4.582575695 + -5 = -0.417424305 t = -0.417424305 Simplifying t = -0.417424305Subproblem 2
t + 5 = -4.582575695 Simplifying t + 5 = -4.582575695 Reorder the terms: 5 + t = -4.582575695 Solving 5 + t = -4.582575695 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + t = -4.582575695 + -5 t = -4.582575695 + -5 Combine like terms: -4.582575695 + -5 = -9.582575695 t = -9.582575695 Simplifying t = -9.582575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.417424305, -9.582575695}
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