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Simplifying 3630t4 + -169645.98t2 + -728375.193 = 0findt Reorder the terms: -728375.193 + -169645.98t2 + 3630t4 = 0findt Anything times zero is zero. -728375.193 + -169645.98t2 + 3630t4 = 0dfint Solving -728375.193 + -169645.98t2 + 3630t4 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3630 the coefficient of the squared term: Divide each side by '3630'. -200.6543231 + -46.73442975t2 + t4 = 0 Move the constant term to the right: Add '200.6543231' to each side of the equation. -200.6543231 + -46.73442975t2 + 200.6543231 + t4 = 0 + 200.6543231 Reorder the terms: -200.6543231 + 200.6543231 + -46.73442975t2 + t4 = 0 + 200.6543231 Combine like terms: -200.6543231 + 200.6543231 = 0.0000000 0.0000000 + -46.73442975t2 + t4 = 0 + 200.6543231 -46.73442975t2 + t4 = 0 + 200.6543231 Combine like terms: 0 + 200.6543231 = 200.6543231 -46.73442975t2 + t4 = 200.6543231 The t term is -46.73442975t2. Take half its coefficient (-23.36721488). Square it (546.0267312) and add it to both sides. Add '546.0267312' to each side of the equation. -46.73442975t2 + 546.0267312 + t4 = 200.6543231 + 546.0267312 Reorder the terms: 546.0267312 + -46.73442975t2 + t4 = 200.6543231 + 546.0267312 Combine like terms: 200.6543231 + 546.0267312 = 746.6810543 546.0267312 + -46.73442975t2 + t4 = 746.6810543 Factor a perfect square on the left side: (t2 + -23.36721488)(t2 + -23.36721488) = 746.6810543 Calculate the square root of the right side: 27.325465308 Break this problem into two subproblems by setting (t2 + -23.36721488) equal to 27.325465308 and -27.325465308.Subproblem 1
t2 + -23.36721488 = 27.325465308 Simplifying t2 + -23.36721488 = 27.325465308 Reorder the terms: -23.36721488 + t2 = 27.325465308 Solving -23.36721488 + t2 = 27.325465308 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23.36721488' to each side of the equation. -23.36721488 + 23.36721488 + t2 = 27.325465308 + 23.36721488 Combine like terms: -23.36721488 + 23.36721488 = 0.00000000 0.00000000 + t2 = 27.325465308 + 23.36721488 t2 = 27.325465308 + 23.36721488 Combine like terms: 27.325465308 + 23.36721488 = 50.692680188 t2 = 50.692680188 Simplifying t2 = 50.692680188 Take the square root of each side: t = {-7.119879226, 7.119879226}Subproblem 2
t2 + -23.36721488 = -27.325465308 Simplifying t2 + -23.36721488 = -27.325465308 Reorder the terms: -23.36721488 + t2 = -27.325465308 Solving -23.36721488 + t2 = -27.325465308 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23.36721488' to each side of the equation. -23.36721488 + 23.36721488 + t2 = -27.325465308 + 23.36721488 Combine like terms: -23.36721488 + 23.36721488 = 0.00000000 0.00000000 + t2 = -27.325465308 + 23.36721488 t2 = -27.325465308 + 23.36721488 Combine like terms: -27.325465308 + 23.36721488 = -3.958250428 t2 = -3.958250428 Simplifying t2 = -3.958250428 Reorder the terms: 3.958250428 + t2 = -3.958250428 + 3.958250428 Combine like terms: -3.958250428 + 3.958250428 = 0.000000000 3.958250428 + t2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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