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Simplifying -5t2 + 100t = 450 Reorder the terms: 100t + -5t2 = 450 Solving 100t + -5t2 = 450 Solving for variable 't'. Reorder the terms: -450 + 100t + -5t2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + 100t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-90 + 20t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-90 + 20t + -1t2)' equal to zero and attempt to solve: Simplifying -90 + 20t + -1t2 = 0 Solving -90 + 20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 90 + -20t + t2 = 0 Move the constant term to the right: Add '-90' to each side of the equation. 90 + -20t + -90 + t2 = 0 + -90 Reorder the terms: 90 + -90 + -20t + t2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -20t + t2 = 0 + -90 -20t + t2 = 0 + -90 Combine like terms: 0 + -90 = -90 -20t + t2 = -90 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -90 + 100 Reorder the terms: 100 + -20t + t2 = -90 + 100 Combine like terms: -90 + 100 = 10 100 + -20t + t2 = 10 Factor a perfect square on the left side: (t + -10)(t + -10) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + -10) equal to 3.16227766 and -3.16227766.Subproblem 1
t + -10 = 3.16227766 Simplifying t + -10 = 3.16227766 Reorder the terms: -10 + t = 3.16227766 Solving -10 + t = 3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + t = 3.16227766 + 10 t = 3.16227766 + 10 Combine like terms: 3.16227766 + 10 = 13.16227766 t = 13.16227766 Simplifying t = 13.16227766Subproblem 2
t + -10 = -3.16227766 Simplifying t + -10 = -3.16227766 Reorder the terms: -10 + t = -3.16227766 Solving -10 + t = -3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -3.16227766 + 10 Combine like terms: -10 + 10 = 0 0 + t = -3.16227766 + 10 t = -3.16227766 + 10 Combine like terms: -3.16227766 + 10 = 6.83772234 t = 6.83772234 Simplifying t = 6.83772234Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.16227766, 6.83772234}Solution
t = {13.16227766, 6.83772234}
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