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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 + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -2t + t2)' equal to zero and attempt to solve: Simplifying -9 + -2t + t2 = 0 Solving -9 + -2t + t2 = 0 Begin completing the square. 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 = 4.16227766 t = 4.16227766 Simplifying t = 4.16227766Subproblem 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 = -2.16227766 t = -2.16227766 Simplifying t = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.16227766, -2.16227766}Solution
t = {4.16227766, -2.16227766}
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