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Simplifying 45 = 10t + 5t2 Solving 45 = 10t + 5t2 Solving for variable 't'. Reorder the terms: 45 + -10t + -5t2 = 10t + -10t + 5t2 + -5t2 Combine like terms: 10t + -10t = 0 45 + -10t + -5t2 = 0 + 5t2 + -5t2 45 + -10t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 45 + -10t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -2t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -2t + -1t2)' equal to zero and attempt to solve: Simplifying 9 + -2t + -1t2 = 0 Solving 9 + -2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 2t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + 2t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t + t2 = 0 + 9 2t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 2t + t2 = 9 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 9 + 1 Reorder the terms: 1 + 2t + t2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2t + t2 = 10 Factor a perfect square on the left side: (t + 1)(t + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
t + 1 = 3.16227766 Simplifying t + 1 = 3.16227766 Reorder the terms: 1 + t = 3.16227766 Solving 1 + t = 3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.16227766 + -1 t = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 t = 2.16227766 Simplifying t = 2.16227766Subproblem 2
t + 1 = -3.16227766 Simplifying t + 1 = -3.16227766 Reorder the terms: 1 + t = -3.16227766 Solving 1 + t = -3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.16227766 + -1 t = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 t = -4.16227766 Simplifying t = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.16227766, -4.16227766}Solution
t = {2.16227766, -4.16227766}
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