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Simplifying 425 = -10t + t2 Solving 425 = -10t + t2 Solving for variable 't'. Reorder the terms: 425 + 10t + -1t2 = -10t + 10t + t2 + -1t2 Combine like terms: -10t + 10t = 0 425 + 10t + -1t2 = 0 + t2 + -1t2 425 + 10t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 425 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -425 + -10t + t2 = 0 Move the constant term to the right: Add '425' to each side of the equation. -425 + -10t + 425 + t2 = 0 + 425 Reorder the terms: -425 + 425 + -10t + t2 = 0 + 425 Combine like terms: -425 + 425 = 0 0 + -10t + t2 = 0 + 425 -10t + t2 = 0 + 425 Combine like terms: 0 + 425 = 425 -10t + t2 = 425 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 = 425 + 25 Reorder the terms: 25 + -10t + t2 = 425 + 25 Combine like terms: 425 + 25 = 450 25 + -10t + t2 = 450 Factor a perfect square on the left side: (t + -5)(t + -5) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (t + -5) equal to 21.213203436 and -21.213203436.Subproblem 1
t + -5 = 21.213203436 Simplifying t + -5 = 21.213203436 Reorder the terms: -5 + t = 21.213203436 Solving -5 + t = 21.213203436 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 = 21.213203436 + 5 Combine like terms: -5 + 5 = 0 0 + t = 21.213203436 + 5 t = 21.213203436 + 5 Combine like terms: 21.213203436 + 5 = 26.213203436 t = 26.213203436 Simplifying t = 26.213203436Subproblem 2
t + -5 = -21.213203436 Simplifying t + -5 = -21.213203436 Reorder the terms: -5 + t = -21.213203436 Solving -5 + t = -21.213203436 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 = -21.213203436 + 5 Combine like terms: -5 + 5 = 0 0 + t = -21.213203436 + 5 t = -21.213203436 + 5 Combine like terms: -21.213203436 + 5 = -16.213203436 t = -16.213203436 Simplifying t = -16.213203436Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.213203436, -16.213203436}
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