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Simplifying 500 + 400t + -10t2 = 0 Solving 500 + 400t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(50 + 40t + -1t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(50 + 40t + -1t2)' equal to zero and attempt to solve: Simplifying 50 + 40t + -1t2 = 0 Solving 50 + 40t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -40t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -40t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + -40t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -40t + t2 = 0 + 50 -40t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 -40t + t2 = 50 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = 50 + 400 Reorder the terms: 400 + -40t + t2 = 50 + 400 Combine like terms: 50 + 400 = 450 400 + -40t + t2 = 450 Factor a perfect square on the left side: (t + -20)(t + -20) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (t + -20) equal to 21.213203436 and -21.213203436.Subproblem 1
t + -20 = 21.213203436 Simplifying t + -20 = 21.213203436 Reorder the terms: -20 + t = 21.213203436 Solving -20 + t = 21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 21.213203436 + 20 Combine like terms: -20 + 20 = 0 0 + t = 21.213203436 + 20 t = 21.213203436 + 20 Combine like terms: 21.213203436 + 20 = 41.213203436 t = 41.213203436 Simplifying t = 41.213203436Subproblem 2
t + -20 = -21.213203436 Simplifying t + -20 = -21.213203436 Reorder the terms: -20 + t = -21.213203436 Solving -20 + t = -21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -21.213203436 + 20 Combine like terms: -20 + 20 = 0 0 + t = -21.213203436 + 20 t = -21.213203436 + 20 Combine like terms: -21.213203436 + 20 = -1.213203436 t = -1.213203436 Simplifying t = -1.213203436Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.213203436, -1.213203436}Solution
t = {41.213203436, -1.213203436}
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