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Simplifying -0.4t2 + 4t + 10 = 1 Reorder the terms: 10 + 4t + -0.4t2 = 1 Solving 10 + 4t + -0.4t2 = 1 Solving for variable 't'. Reorder the terms: 10 + -1 + 4t + -0.4t2 = 1 + -1 Combine like terms: 10 + -1 = 9 9 + 4t + -0.4t2 = 1 + -1 Combine like terms: 1 + -1 = 0 9 + 4t + -0.4t2 = 0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -22.5 + -10t + t2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -10t + 22.5 + t2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -10t + t2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -10t + t2 = 0 + 22.5 -10t + t2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -10t + t2 = 22.5 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 22.5 + 25 Reorder the terms: 25 + -10t + t2 = 22.5 + 25 Combine like terms: 22.5 + 25 = 47.5 25 + -10t + t2 = 47.5 Factor a perfect square on the left side: (t + -5)(t + -5) = 47.5 Calculate the square root of the right side: 6.892024376 Break this problem into two subproblems by setting (t + -5) equal to 6.892024376 and -6.892024376.Subproblem 1
t + -5 = 6.892024376 Simplifying t + -5 = 6.892024376 Reorder the terms: -5 + t = 6.892024376 Solving -5 + t = 6.892024376 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 6.892024376 + 5 Combine like terms: -5 + 5 = 0 0 + t = 6.892024376 + 5 t = 6.892024376 + 5 Combine like terms: 6.892024376 + 5 = 11.892024376 t = 11.892024376 Simplifying t = 11.892024376Subproblem 2
t + -5 = -6.892024376 Simplifying t + -5 = -6.892024376 Reorder the terms: -5 + t = -6.892024376 Solving -5 + t = -6.892024376 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -6.892024376 + 5 Combine like terms: -5 + 5 = 0 0 + t = -6.892024376 + 5 t = -6.892024376 + 5 Combine like terms: -6.892024376 + 5 = -1.892024376 t = -1.892024376 Simplifying t = -1.892024376Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.892024376, -1.892024376}
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