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Simplifying 29 = 62t + -5t2 Solving 29 = 62t + -5t2 Solving for variable 't'. Reorder the terms: 29 + -62t + 5t2 = 62t + -62t + -5t2 + 5t2 Combine like terms: 62t + -62t = 0 29 + -62t + 5t2 = 0 + -5t2 + 5t2 29 + -62t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 29 + -62t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.8 + -12.4t + t2 = 0 Move the constant term to the right: Add '-5.8' to each side of the equation. 5.8 + -12.4t + -5.8 + t2 = 0 + -5.8 Reorder the terms: 5.8 + -5.8 + -12.4t + t2 = 0 + -5.8 Combine like terms: 5.8 + -5.8 = 0.0 0.0 + -12.4t + t2 = 0 + -5.8 -12.4t + t2 = 0 + -5.8 Combine like terms: 0 + -5.8 = -5.8 -12.4t + t2 = -5.8 The t term is -12.4t. Take half its coefficient (-6.2). Square it (38.44) and add it to both sides. Add '38.44' to each side of the equation. -12.4t + 38.44 + t2 = -5.8 + 38.44 Reorder the terms: 38.44 + -12.4t + t2 = -5.8 + 38.44 Combine like terms: -5.8 + 38.44 = 32.64 38.44 + -12.4t + t2 = 32.64 Factor a perfect square on the left side: (t + -6.2)(t + -6.2) = 32.64 Calculate the square root of the right side: 5.713142743 Break this problem into two subproblems by setting (t + -6.2) equal to 5.713142743 and -5.713142743.Subproblem 1
t + -6.2 = 5.713142743 Simplifying t + -6.2 = 5.713142743 Reorder the terms: -6.2 + t = 5.713142743 Solving -6.2 + t = 5.713142743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + t = 5.713142743 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + t = 5.713142743 + 6.2 t = 5.713142743 + 6.2 Combine like terms: 5.713142743 + 6.2 = 11.913142743 t = 11.913142743 Simplifying t = 11.913142743Subproblem 2
t + -6.2 = -5.713142743 Simplifying t + -6.2 = -5.713142743 Reorder the terms: -6.2 + t = -5.713142743 Solving -6.2 + t = -5.713142743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + t = -5.713142743 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + t = -5.713142743 + 6.2 t = -5.713142743 + 6.2 Combine like terms: -5.713142743 + 6.2 = 0.486857257 t = 0.486857257 Simplifying t = 0.486857257Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.913142743, 0.486857257}
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