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Simplifying 4.4375 = t + t2 Solving 4.4375 = t + t2 Solving for variable 't'. Reorder the terms: 4.4375 + -1t + -1t2 = t + -1t + t2 + -1t2 Combine like terms: t + -1t = 0 4.4375 + -1t + -1t2 = 0 + t2 + -1t2 4.4375 + -1t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 4.4375 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4.4375 + t + t2 = 0 Move the constant term to the right: Add '4.4375' to each side of the equation. -4.4375 + t + 4.4375 + t2 = 0 + 4.4375 Reorder the terms: -4.4375 + 4.4375 + t + t2 = 0 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + t + t2 = 0 + 4.4375 t + t2 = 0 + 4.4375 Combine like terms: 0 + 4.4375 = 4.4375 t + t2 = 4.4375 The t term is t. 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. + 0.25 + t2 = 4.4375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 4.4375 + 0.25 Combine like terms: 4.4375 + 0.25 = 4.6875 1.25 + t2 = 4.6875 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 4.6875 Calculate the square root of the right side: 2.165063509 Break this problem into two subproblems by setting (t + 0.5) equal to 2.165063509 and -2.165063509.Subproblem 1
t + 0.5 = 2.165063509 Simplifying t + 0.5 = 2.165063509 Reorder the terms: 0.5 + t = 2.165063509 Solving 0.5 + t = 2.165063509 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 = 2.165063509 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.165063509 + -0.5 t = 2.165063509 + -0.5 Combine like terms: 2.165063509 + -0.5 = 1.665063509 t = 1.665063509 Simplifying t = 1.665063509Subproblem 2
t + 0.5 = -2.165063509 Simplifying t + 0.5 = -2.165063509 Reorder the terms: 0.5 + t = -2.165063509 Solving 0.5 + t = -2.165063509 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 = -2.165063509 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.165063509 + -0.5 t = -2.165063509 + -0.5 Combine like terms: -2.165063509 + -0.5 = -2.665063509 t = -2.665063509 Simplifying t = -2.665063509Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.665063509, -2.665063509}
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