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Simplifying 4t2 + -4t + -45 = 0 Reorder the terms: -45 + -4t + 4t2 = 0 Solving -45 + -4t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -1t + t2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -1t + 11.25 + t2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -1t + t2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -1t + t2 = 0 + 11.25 -1t + t2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -1t + t2 = 11.25 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 11.25 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 11.25 + 0.25 Combine like terms: 11.25 + 0.25 = 11.5 0.25 + -1t + t2 = 11.5 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (t + -0.5) equal to 3.391164992 and -3.391164992.Subproblem 1
t + -0.5 = 3.391164992 Simplifying t + -0.5 = 3.391164992 Reorder the terms: -0.5 + t = 3.391164992 Solving -0.5 + t = 3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 3.391164992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 3.391164992 + 0.5 t = 3.391164992 + 0.5 Combine like terms: 3.391164992 + 0.5 = 3.891164992 t = 3.891164992 Simplifying t = 3.891164992Subproblem 2
t + -0.5 = -3.391164992 Simplifying t + -0.5 = -3.391164992 Reorder the terms: -0.5 + t = -3.391164992 Solving -0.5 + t = -3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -3.391164992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -3.391164992 + 0.5 t = -3.391164992 + 0.5 Combine like terms: -3.391164992 + 0.5 = -2.891164992 t = -2.891164992 Simplifying t = -2.891164992Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.891164992, -2.891164992}
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