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Simplifying -1t2 + 35t + 42 = 0 Reorder the terms: 42 + 35t + -1t2 = 0 Solving 42 + 35t + -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'. -42 + -35t + t2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -35t + 42 + t2 = 0 + 42 Reorder the terms: -42 + 42 + -35t + t2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -35t + t2 = 0 + 42 -35t + t2 = 0 + 42 Combine like terms: 0 + 42 = 42 -35t + t2 = 42 The t term is -35t. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35t + 306.25 + t2 = 42 + 306.25 Reorder the terms: 306.25 + -35t + t2 = 42 + 306.25 Combine like terms: 42 + 306.25 = 348.25 306.25 + -35t + t2 = 348.25 Factor a perfect square on the left side: (t + -17.5)(t + -17.5) = 348.25 Calculate the square root of the right side: 18.661457607 Break this problem into two subproblems by setting (t + -17.5) equal to 18.661457607 and -18.661457607.Subproblem 1
t + -17.5 = 18.661457607 Simplifying t + -17.5 = 18.661457607 Reorder the terms: -17.5 + t = 18.661457607 Solving -17.5 + t = 18.661457607 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = 18.661457607 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = 18.661457607 + 17.5 t = 18.661457607 + 17.5 Combine like terms: 18.661457607 + 17.5 = 36.161457607 t = 36.161457607 Simplifying t = 36.161457607Subproblem 2
t + -17.5 = -18.661457607 Simplifying t + -17.5 = -18.661457607 Reorder the terms: -17.5 + t = -18.661457607 Solving -17.5 + t = -18.661457607 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = -18.661457607 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = -18.661457607 + 17.5 t = -18.661457607 + 17.5 Combine like terms: -18.661457607 + 17.5 = -1.161457607 t = -1.161457607 Simplifying t = -1.161457607Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.161457607, -1.161457607}
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