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Simplifying 4t2 + -7t + -3 = 0 Reorder the terms: -3 + -7t + 4t2 = 0 Solving -3 + -7t + 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'. -0.75 + -1.75t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.75t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.75t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.75t + t2 = 0 + 0.75 -1.75t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.75t + t2 = 0.75 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = 0.75 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 0.75 + 0.765625 Combine like terms: 0.75 + 0.765625 = 1.515625 0.765625 + -1.75t + t2 = 1.515625 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (t + -0.875) equal to 1.231107225 and -1.231107225.Subproblem 1
t + -0.875 = 1.231107225 Simplifying t + -0.875 = 1.231107225 Reorder the terms: -0.875 + t = 1.231107225 Solving -0.875 + t = 1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 1.231107225 + 0.875 t = 1.231107225 + 0.875 Combine like terms: 1.231107225 + 0.875 = 2.106107225 t = 2.106107225 Simplifying t = 2.106107225Subproblem 2
t + -0.875 = -1.231107225 Simplifying t + -0.875 = -1.231107225 Reorder the terms: -0.875 + t = -1.231107225 Solving -0.875 + t = -1.231107225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -1.231107225 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -1.231107225 + 0.875 t = -1.231107225 + 0.875 Combine like terms: -1.231107225 + 0.875 = -0.356107225 t = -0.356107225 Simplifying t = -0.356107225Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.106107225, -0.356107225}
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