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Simplifying 4t2 + 7t + 2 = 0 Reorder the terms: 2 + 7t + 4t2 = 0 Solving 2 + 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'. 0.5 + 1.75t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.75t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.75t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.75t + t2 = 0 + -0.5 1.75t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.75t + t2 = -0.5 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 = -0.5 + 0.765625 Reorder the terms: 0.765625 + 1.75t + t2 = -0.5 + 0.765625 Combine like terms: -0.5 + 0.765625 = 0.265625 0.765625 + 1.75t + t2 = 0.265625 Factor a perfect square on the left side: (t + 0.875)(t + 0.875) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (t + 0.875) equal to 0.515388203 and -0.515388203.Subproblem 1
t + 0.875 = 0.515388203 Simplifying t + 0.875 = 0.515388203 Reorder the terms: 0.875 + t = 0.515388203 Solving 0.875 + t = 0.515388203 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 = 0.515388203 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + t = 0.515388203 + -0.875 t = 0.515388203 + -0.875 Combine like terms: 0.515388203 + -0.875 = -0.359611797 t = -0.359611797 Simplifying t = -0.359611797Subproblem 2
t + 0.875 = -0.515388203 Simplifying t + 0.875 = -0.515388203 Reorder the terms: 0.875 + t = -0.515388203 Solving 0.875 + t = -0.515388203 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 = -0.515388203 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + t = -0.515388203 + -0.875 t = -0.515388203 + -0.875 Combine like terms: -0.515388203 + -0.875 = -1.390388203 t = -1.390388203 Simplifying t = -1.390388203Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.359611797, -1.390388203}
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