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Simplifying t2 + 50t + -150 = 0 Reorder the terms: -150 + 50t + t2 = 0 Solving -150 + 50t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 50t + 150 + t2 = 0 + 150 Reorder the terms: -150 + 150 + 50t + t2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 50t + t2 = 0 + 150 50t + t2 = 0 + 150 Combine like terms: 0 + 150 = 150 50t + t2 = 150 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 150 + 625 Reorder the terms: 625 + 50t + t2 = 150 + 625 Combine like terms: 150 + 625 = 775 625 + 50t + t2 = 775 Factor a perfect square on the left side: (t + 25)(t + 25) = 775 Calculate the square root of the right side: 27.838821814 Break this problem into two subproblems by setting (t + 25) equal to 27.838821814 and -27.838821814.Subproblem 1
t + 25 = 27.838821814 Simplifying t + 25 = 27.838821814 Reorder the terms: 25 + t = 27.838821814 Solving 25 + t = 27.838821814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 27.838821814 + -25 Combine like terms: 25 + -25 = 0 0 + t = 27.838821814 + -25 t = 27.838821814 + -25 Combine like terms: 27.838821814 + -25 = 2.838821814 t = 2.838821814 Simplifying t = 2.838821814Subproblem 2
t + 25 = -27.838821814 Simplifying t + 25 = -27.838821814 Reorder the terms: 25 + t = -27.838821814 Solving 25 + t = -27.838821814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -27.838821814 + -25 Combine like terms: 25 + -25 = 0 0 + t = -27.838821814 + -25 t = -27.838821814 + -25 Combine like terms: -27.838821814 + -25 = -52.838821814 t = -52.838821814 Simplifying t = -52.838821814Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.838821814, -52.838821814}
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