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Simplifying t2 + -1t + -110 = 110 Reorder the terms: -110 + -1t + t2 = 110 Solving -110 + -1t + t2 = 110 Solving for variable 't'. Reorder the terms: -110 + -110 + -1t + t2 = 110 + -110 Combine like terms: -110 + -110 = -220 -220 + -1t + t2 = 110 + -110 Combine like terms: 110 + -110 = 0 -220 + -1t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + -1t + 220 + t2 = 0 + 220 Reorder the terms: -220 + 220 + -1t + t2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -1t + t2 = 0 + 220 -1t + t2 = 0 + 220 Combine like terms: 0 + 220 = 220 -1t + t2 = 220 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 220 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 220 + 0.25 Combine like terms: 220 + 0.25 = 220.25 0.25 + -1t + t2 = 220.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (t + -0.5) equal to 14.84082208 and -14.84082208.Subproblem 1
t + -0.5 = 14.84082208 Simplifying t + -0.5 = 14.84082208 Reorder the terms: -0.5 + t = 14.84082208 Solving -0.5 + t = 14.84082208 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 14.84082208 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 14.84082208 + 0.5 t = 14.84082208 + 0.5 Combine like terms: 14.84082208 + 0.5 = 15.34082208 t = 15.34082208 Simplifying t = 15.34082208Subproblem 2
t + -0.5 = -14.84082208 Simplifying t + -0.5 = -14.84082208 Reorder the terms: -0.5 + t = -14.84082208 Solving -0.5 + t = -14.84082208 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -14.84082208 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -14.84082208 + 0.5 t = -14.84082208 + 0.5 Combine like terms: -14.84082208 + 0.5 = -14.34082208 t = -14.34082208 Simplifying t = -14.34082208Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.34082208, -14.34082208}
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