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Simplifying 2t2 + -3t = 10 Reorder the terms: -3t + 2t2 = 10 Solving -3t + 2t2 = 10 Solving for variable 't'. Reorder the terms: -10 + -3t + 2t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -1.5t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.5t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -1.5t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.5t + t2 = 0 + 5 -1.5t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.5t + t2 = 5 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 5 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 5 + 0.5625 Combine like terms: 5 + 0.5625 = 5.5625 0.5625 + -1.5t + t2 = 5.5625 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (t + -0.75) equal to 2.358495283 and -2.358495283.Subproblem 1
t + -0.75 = 2.358495283 Simplifying t + -0.75 = 2.358495283 Reorder the terms: -0.75 + t = 2.358495283 Solving -0.75 + t = 2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 2.358495283 + 0.75 t = 2.358495283 + 0.75 Combine like terms: 2.358495283 + 0.75 = 3.108495283 t = 3.108495283 Simplifying t = 3.108495283Subproblem 2
t + -0.75 = -2.358495283 Simplifying t + -0.75 = -2.358495283 Reorder the terms: -0.75 + t = -2.358495283 Solving -0.75 + t = -2.358495283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -2.358495283 + 0.75 t = -2.358495283 + 0.75 Combine like terms: -2.358495283 + 0.75 = -1.608495283 t = -1.608495283 Simplifying t = -1.608495283Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.108495283, -1.608495283}
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